Initial planning tool (#1753)

We need to optimize the prompt, but this causes the model to use the new
planning_tool.

<img width="765" height="110" alt="image"
src="https://github.com/user-attachments/assets/45633f7f-3c85-4e60-8b80-902f1b3b508d"
/>

codex-rs/core/prompt.md

@@ -96,3 +96,12 @@ You can invoke apply_patch like:
 ```
 shell {"command":["apply_patch","*** Begin Patch\n*** Add File: hello.txt\n+Hello, world!\n*** End Patch\n"]}
 ```
+
+Plan updates
+
+A tool named `update_plan` is available. Use it to keep an up‑to‑date, step‑by‑step plan for the task so you can follow your progress. When making your plans, keep in mind that you are a deployed coding agent - `update_plan` calls should not involve doing anything that you aren't capable of doing. For example, `update_plan` calls should NEVER contain tasks to merge your own pull requests. Only stop to ask the user if you genuinely need their feedback on a change.
+
+- At the start of the task, call `update_plan` with an initial plan: a short list of 1‑sentence steps with a `status` for each step (`pending`, `in_progress`, or `completed`). There should always be exactly one `in_progress` step until everything is done.
+- Whenever you finish a step, call `update_plan` again, marking the finished step as `completed` and the next step as `in_progress`.
+- If your plan needs to change, call `update_plan` with the revised steps and include an `explanation` describing the change.
+- When all steps are complete, make a final `update_plan` call with all steps marked `completed`.