[feat] Support cross turn token in after last user message.

[guapisolo]

Motivation

Modifications

Accuracy Tests

Benchmarking and Profiling

Checklist

• Format your code according to the Format code with pre-commit.
• Add unit tests according to the Run and add unit tests.
• Update documentation according to Write documentations.
• Provide accuracy and speed benchmark results according to Test the accuracy and Benchmark the speed.
• Follow the SGLang code style guidance.

Review Process

1. Ping Merge Oncalls to start the PR flow. See the PR Merge Process.
2. Get approvals from CODEOWNERS and other reviewers.
3. Trigger CI tests with comments or contact authorized users to do so.
   • /tag-run-ci-label, /rerun-failed-ci, /tag-and-rerun-ci
4. After green CI and required approvals, ask Merge Oncalls to merge.

[gemini-code-assist]

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