Long-running planning tasks timeout and fail

Describe the bug
When using the agent for complex scenarios requiring extended planning time (during "writing-plans" phase), the process hangs and eventually fails due to API timeout errors before completion.
To Reproduce
Steps to reproduce the behavior:

1. Start a complex task that requires detailed planning
2. Agent enters "writing-plans" phase
3. Wait for 20m
4. See operation interrupted with timeout error
5. Planning progress is lost, need to restart from beginning

Expected behavior
Agent should handle long-running planning tasks more gracefully, either by:

• Extending timeout for complex operations
• Implementing progress persistence to resume interrupted planning
• Breaking down planning into smaller chunks

Additional context
The "writing-plans" task generates the entire plan in one single output, which takes too long for complex scenarios and causes timeout. Could the task be split into smaller chunks or streamed incrementally instead of generating everything at once?

Start by reproducing a complex task that enters the "writing-plans" phase and runs for about 20 minutes, then trace how the single plan output interacts with API timeouts. Compare timeout handling, progress persistence, and incremental chunking, and consider the work done when planning no longer fails or loses progress on long-running tasks.