test(agent): cover the codex iteration-summary retry path

Iteration-limit summaries retry once when the first attempt comes back empty.
Both attempts share one builder closure, so assert the retry body is as
tool-free as the first: forces an empty summary, then checks every captured
codex request for tools / tool_choice / parallel_tool_calls.

Addresses the retry-coverage request on #32777.

tests/run_agent/test_run_agent.py

@@ -2947,6 +2947,58 @@ class TestHandleMaxIterations:
         assert "tool_choice" not in captured
         assert "parallel_tool_calls" not in captured
 
+    def test_codex_summary_retry_also_strips_tool_controls(self, agent):
+        """The retry attempt must be as toolless as the first one.
+
+        Iteration-limit summaries retry once when the first summary comes back empty; both
+        attempts build their body through the same codex path, so both must drop the tool-control
+        block the transport emits alongside ``tools`` (agent/transports/codex.py).
+        """
+        agent.api_mode = "codex_responses"
+        agent.provider = "openai-codex"
+        agent.base_url = "https://chatgpt.com/backend-api/codex"
+        agent._base_url_lower = agent.base_url.lower()
+        agent._base_url_hostname = "chatgpt.com"
+        agent.model = "gpt-5.5"
+        agent._cached_system_prompt = "You are helpful."
+
+        bodies = []
+        tool_laden = {
+            "model": "gpt-5.5",
+            "input": [{"role": "user", "content": "do stuff"}],
+            "tools": [{"type": "function", "name": "web_search"}],
+            "tool_choice": "auto",
+            "parallel_tool_calls": True,
+        }
+
+        def fake_run_codex_stream(kwargs):
+            bodies.append(dict(kwargs))
+            # First attempt returns an empty summary so the caller takes the retry path.
+            text = "" if len(bodies) == 1 else "Summary"
+            return SimpleNamespace(
+                status="completed",
+                output=[
+                    SimpleNamespace(
+                        type="message",
+                        status="completed",
+                        content=[SimpleNamespace(type="output_text", text=text)],
+                    )
+                ],
+            )
+
+        with (
+            patch.object(agent, "_build_api_kwargs", return_value=tool_laden.copy()),
+            patch.object(agent, "_run_codex_stream", side_effect=fake_run_codex_stream),
+        ):
+            result = agent._handle_max_iterations([{"role": "user", "content": "do stuff"}], 90)
+
+        assert result == "Summary"
+        assert len(bodies) == 2, f"expected one retry after the empty summary, got {len(bodies)} attempts"
+        for attempt_index, sent in enumerate(bodies):
+            assert "tools" not in sent, f"attempt {attempt_index}: tools leaked into the summary call"
+            assert "tool_choice" not in sent, f"attempt {attempt_index}: tool_choice leaked"
+            assert "parallel_tool_calls" not in sent, f"attempt {attempt_index}: parallel_tool_calls leaked"
+
     def test_api_sanitizer_matches_responses_call_id_when_id_differs(self, agent):
         messages = [
             {