#skip-bb
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<!-- This is an auto-generated description by cubic. -->
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## Summary by cubic
Fixes the PR review responder so pushes go to the PR’s fork instead of
the base repo on forked PRs. Exposes the head repository and sets
origin’s pushurl to ensure correct push behavior.

- **Bug Fixes**
- Exposes head_repo from workflow_run (run.head_repository.full_name)
for later steps.
- Adds a step to set origin’s pushurl to the PR’s head repo using
GITHUB_TOKEN, preventing accidental pushes to the base repo after
claude-code-action rewrites origin.

<sup>Written for commit 9ca429753073a667b554987f3ab3e6f03a14355b.
Summary will update on new commits.</sup>

<!-- End of auto-generated description by cubic. -->
Co-authored-by: Will Chen <willchen90@gmail.com>