chore: add multi-turn example code

[Wendong-Fan]

Description

Describe your changes in detail (optional if the linked issue already contains a detailed description of the changes).

Checklist

Go over all the following points, and put an x in all the boxes that apply.

• I have read the CONTRIBUTION guide (required)
• I have linked this PR to an issue using the Development section on the right sidebar or by adding Fixes #issue-number in the PR description (required)
• I have checked if any dependencies need to be added or updated in pyproject.toml and uv lock
• I have updated the tests accordingly (required for a bug fix or a new feature)
• I have updated the documentation if needed:
• I have added examples if this is a new feature

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✨ Finishing touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch multi_turn_example

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[a7m-1st]

Thanks @Wendong-Fan !