diff --git a/.github/workflows/amd64_linux_bazel.yml b/.github/workflows/amd64_linux_bazel.yml
index 01e1e7d741..03047b68f2 100644
--- a/.github/workflows/amd64_linux_bazel.yml
+++ b/.github/workflows/amd64_linux_bazel.yml
@@ -27,7 +27,7 @@ jobs:
       - name: Check mvn
         run: mvn --version
       - name: Setup Python
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python.version }}
       - name: Check Python
diff --git a/.github/workflows/amd64_linux_cmake_python.yml b/.github/workflows/amd64_linux_cmake_python.yml
index 20c6d90fea..7727d62083 100644
--- a/.github/workflows/amd64_linux_cmake_python.yml
+++ b/.github/workflows/amd64_linux_cmake_python.yml
@@ -34,7 +34,7 @@ jobs:
           sudo apt install -y swig
           swig -version
       - name: Setup Python
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python.version }}
       - name: Update Path
diff --git a/.github/workflows/amd64_macos_bazel.yml b/.github/workflows/amd64_macos_bazel.yml
index c493c6aee9..22206d0101 100644
--- a/.github/workflows/amd64_macos_bazel.yml
+++ b/.github/workflows/amd64_macos_bazel.yml
@@ -27,7 +27,7 @@ jobs:
       - name: Check mvn
         run: mvn --version
       - name: Setup Python
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python.version }}
       - name: Check Python
diff --git a/.github/workflows/amd64_macos_cmake_python.yml b/.github/workflows/amd64_macos_cmake_python.yml
index 072d573c71..0c967c590c 100644
--- a/.github/workflows/amd64_macos_cmake_python.yml
+++ b/.github/workflows/amd64_macos_cmake_python.yml
@@ -29,7 +29,7 @@ jobs:
           brew install swig
           swig -version
       - name: Setup Python
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python.version }}
       - name: Update Path
diff --git a/.github/workflows/amd64_windows_bazel.yml b/.github/workflows/amd64_windows_bazel.yml
index fa5f08bd35..b5b406157a 100644
--- a/.github/workflows/amd64_windows_bazel.yml
+++ b/.github/workflows/amd64_windows_bazel.yml
@@ -29,7 +29,7 @@ jobs:
       - name: Check mvn
         run: mvn --version
       - name: Setup Python
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python.version }}
       - name: Check Python
diff --git a/.github/workflows/amd64_windows_cmake_python.yml b/.github/workflows/amd64_windows_cmake_python.yml
index 0b6191ccf0..e6b61c88f8 100644
--- a/.github/workflows/amd64_windows_cmake_python.yml
+++ b/.github/workflows/amd64_windows_cmake_python.yml
@@ -25,7 +25,7 @@ jobs:
       CTEST_OUTPUT_ON_FAILURE: 1
     steps:
       - uses: actions/checkout@v4
-      - uses: actions/setup-python@v4
+      - uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python.version }}
       - name: Install python3
diff --git a/.github/workflows/arm64_macos_bazel.yml b/.github/workflows/arm64_macos_bazel.yml
index c0dd6bafdd..7f9fcdfe76 100644
--- a/.github/workflows/arm64_macos_bazel.yml
+++ b/.github/workflows/arm64_macos_bazel.yml
@@ -27,7 +27,7 @@ jobs:
       - name: Check mvn
         run: mvn --version
       - name: Setup Python
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python.version }}
       - name: Check Python
diff --git a/.github/workflows/arm64_macos_cmake_python.yml b/.github/workflows/arm64_macos_cmake_python.yml
index 5de445d2fe..1ff8604f3a 100644
--- a/.github/workflows/arm64_macos_cmake_python.yml
+++ b/.github/workflows/arm64_macos_cmake_python.yml
@@ -29,7 +29,7 @@ jobs:
           brew install swig
           swig -version
       - name: Setup Python
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python.version }}
       - name: Update Path
diff --git a/ortools/graph/christofides.h b/ortools/graph/christofides.h
index 92bd1bfcce..9f7071a8aa 100644
--- a/ortools/graph/christofides.h
+++ b/ortools/graph/christofides.h
@@ -28,6 +28,7 @@
 
 #include <cstdint>
 #include <functional>
+#include <string>
 #include <type_traits>
 #include <utility>
 #include <vector>
diff --git a/ortools/graph/cliques.h b/ortools/graph/cliques.h
index 702a0a0909..130835ad79 100644
--- a/ortools/graph/cliques.h
+++ b/ortools/graph/cliques.h
@@ -30,6 +30,7 @@
 #include <limits>
 #include <numeric>
 #include <string>
+#include <utility>
 #include <vector>
 
 #include "absl/strings/str_cat.h"
diff --git a/ortools/sat/cp_model_solver_helpers.h b/ortools/sat/cp_model_solver_helpers.h
index 915bd91c17..d3fe19b03c 100644
--- a/ortools/sat/cp_model_solver_helpers.h
+++ b/ortools/sat/cp_model_solver_helpers.h
@@ -18,6 +18,7 @@
 #include <memory>
 #include <string>
 #include <tuple>
+#include <utility>
 #include <vector>
 
 #include "absl/flags/declare.h"
diff --git a/ortools/sat/cuts.h b/ortools/sat/cuts.h
index 28359dc474..cc0ec7dbfb 100644
--- a/ortools/sat/cuts.h
+++ b/ortools/sat/cuts.h
@@ -18,9 +18,12 @@
 
 #include <algorithm>
 #include <array>
+#include <cmath>
+#include <cstdlib>
 #include <functional>
 #include <limits>
 #include <string>
+#include <tuple>
 #include <utility>
 #include <vector>
 
diff --git a/ortools/sat/disjunctive.h b/ortools/sat/disjunctive.h
index efe214257e..70812a4c0a 100644
--- a/ortools/sat/disjunctive.h
+++ b/ortools/sat/disjunctive.h
@@ -17,6 +17,8 @@
 #include <algorithm>
 #include <functional>
 #include <memory>
+#include <string>
+#include <utility>
 #include <vector>
 
 #include "absl/types/span.h"
diff --git a/ortools/sat/precedences.h b/ortools/sat/precedences.h
index 2e984f41cf..2ac790a13f 100644
--- a/ortools/sat/precedences.h
+++ b/ortools/sat/precedences.h
@@ -18,6 +18,7 @@
 #include <cstdint>
 #include <deque>
 #include <functional>
+#include <memory>
 #include <utility>
 #include <vector>
 
diff --git a/ortools/sat/util.h b/ortools/sat/util.h
index 29a35b7ac3..9098f8c2a8 100644
--- a/ortools/sat/util.h
+++ b/ortools/sat/util.h
@@ -19,6 +19,7 @@
 #include <cstdint>
 #include <deque>
 #include <limits>
+#include <memory>
 #include <string>
 #include <type_traits>
 #include <utility>
diff --git a/ortools/sat/work_assignment.cc b/ortools/sat/work_assignment.cc
index a7cec47382..712cf9cfe3 100644
--- a/ortools/sat/work_assignment.cc
+++ b/ortools/sat/work_assignment.cc
@@ -159,6 +159,8 @@ std::optional<ProtoLiteral> ProtoLiteral::EncodeLiteral(
   return result;
 }
 
+ProtoTrail::ProtoTrail() { target_phase_.reserve(kMaxPhaseSize); }
+
 void ProtoTrail::PushLevel(const ProtoLiteral& decision,
                            IntegerValue objective_lb, int node_id) {
   CHECK_GT(node_id, 0);
@@ -793,8 +795,8 @@ bool SharedTreeWorker::SyncWithSharedTree() {
   if (ShouldReplaceSubtree()) {
     ++num_trees_;
     VLOG(2) << parameters_->name() << " acquiring tree #" << num_trees_
-            << " after " << num_restarts_ - tree_assignment_restart_
-            << " restarts prev depth: " << assigned_tree_.MaxLevel()
+            << " after " << restart_policy_->NumRestarts() << " restarts"
+            << " prev depth: " << assigned_tree_.MaxLevel()
             << " target: " << assigned_tree_lbds_.WindowAverage()
             << " lbd: " << restart_policy_->LbdAverageSinceReset();
     if (parameters_->shared_tree_worker_enable_phase_sharing() &&
@@ -806,11 +808,10 @@ bool SharedTreeWorker::SyncWithSharedTree() {
         // workers.
         auto encoded = ProtoLiteral::EncodeLiteral(lit, mapping_);
         if (!encoded.has_value()) continue;
-        assigned_tree_.SetPhase(*encoded);
+        if (!assigned_tree_.AddPhase(*encoded)) break;
       }
     }
     manager_->ReplaceTree(assigned_tree_);
-    tree_assignment_restart_ = num_restarts_;
     assigned_tree_lbds_.Add(restart_policy_->LbdAverageSinceReset());
     restart_policy_->Reset();
     if (parameters_->shared_tree_worker_enable_phase_sharing()) {
@@ -856,9 +857,8 @@ SatSolver::Status SharedTreeWorker::Search(
       return sat_solver_->UnsatStatus();
     }
     if (heuristics_->restart_policies[heuristics_->policy_index]()) {
-      ++num_restarts_;
-      heuristics_->policy_index =
-          num_restarts_ % heuristics_->decision_policies.size();
+      heuristics_->policy_index = restart_policy_->NumRestarts() %
+                                  heuristics_->decision_policies.size();
       sat_solver_->Backtrack(0);
     }
     if (!SyncWithLocalTrail()) return sat_solver_->UnsatStatus();
diff --git a/ortools/sat/work_assignment.h b/ortools/sat/work_assignment.h
index 6f5119b9e9..162b2ec648 100644
--- a/ortools/sat/work_assignment.h
+++ b/ortools/sat/work_assignment.h
@@ -102,6 +102,8 @@ class ProtoLiteral {
 // implications may be propagated.
 class ProtoTrail {
  public:
+  ProtoTrail();
+
   // Adds a new assigned level to the trail.
   void PushLevel(const ProtoLiteral& decision, IntegerValue objective_lb,
                  int node_id);
@@ -147,18 +149,25 @@ class ProtoTrail {
 
   const std::vector<ProtoLiteral>& TargetPhase() const { return target_phase_; }
   void ClearTargetPhase() { target_phase_.clear(); }
-  void SetPhase(const ProtoLiteral& lit) {
-    if (implication_level_.contains(lit)) return;
-    target_phase_.push_back(lit);
+  // Appends a literal to the target phase, returns false if the phase is full.
+  bool AddPhase(const ProtoLiteral& lit) {
+    if (target_phase_.size() >= kMaxPhaseSize) return false;
+    if (!implication_level_.contains(lit)) {
+      target_phase_.push_back(lit);
+    }
+    return true;
   }
   void SetTargetPhase(absl::Span<const ProtoLiteral> phase) {
     ClearTargetPhase();
     for (const ProtoLiteral& lit : phase) {
-      SetPhase(lit);
+      if (!AddPhase(lit)) break;
     }
   }
 
  private:
+  // 256 ProtoLiterals take up 4KiB
+  static constexpr int kMaxPhaseSize = 256;
+
   std::vector<ProtoLiteral>& MutableImplications(int level) {
     return implications_[level - 1];
   }
@@ -335,14 +344,11 @@ class SharedTreeWorker {
   LevelZeroCallbackHelper* level_zero_callbacks_;
   RevIntRepository* reversible_int_repository_;
 
-  int64_t num_restarts_ = 0;
   int64_t num_trees_ = 0;
 
   ProtoTrail assigned_tree_;
   std::vector<Literal> assigned_tree_literals_;
   std::vector<std::vector<Literal>> assigned_tree_implications_;
-  // How many restarts had happened when the current tree was assigned?
-  int64_t tree_assignment_restart_ = -1;
 
   // True if the last decision may split the assigned tree and has not yet been
   // proposed to the SharedTreeManager.
diff --git a/ortools/sat/work_assignment_test.cc b/ortools/sat/work_assignment_test.cc
index b26417cc2e..cda049d48c 100644
--- a/ortools/sat/work_assignment_test.cc
+++ b/ortools/sat/work_assignment_test.cc
@@ -564,7 +564,7 @@ TEST(SharedTreeManagerTest, TrailSharing) {
   trail1.AddImplication(1, ProtoLiteral(1, 1));
   trail1.AddImplication(1, ProtoLiteral(1, 3));
   shared_tree_manager->SyncTree(trail1);
-  trail1.SetPhase(ProtoLiteral(2, 1));
+  trail1.AddPhase(ProtoLiteral(2, 1));
   shared_tree_manager->ReplaceTree(trail1);
   shared_tree_manager->ReplaceTree(trail2);