When the model answers beside a housekeeping tool call (memory, todo_list,
skill_manage, session_search) and the follow-up is empty, the turn ends on
that pre-tool answer (fallback_prior_turn_content, since #10472). The final
then repeats text the client already streamed before the tool, but nothing on
the wire says so: message.complete looks like a new response.
Record the reuse where it happens (the housekeeping fallback and the
budget-exhaustion reuse of a previewed verification candidate), report
response_reused only when the final still equals that text (a footer or
explanation appended later drops it), and carry it on message.complete.
Never inferred from equal text: "Done." / tool / "Done." are two responses.
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