Inline reasoning tags in an assistant message's content field leak to every downstream consumer: messaging platforms (#8878, #9568), API replay of prior turns, session transcript, CLI recap, generated session titles, and context compression. _extract_reasoning() already captures the reasoning text into msg['reasoning'] separately, so the raw tags in content are redundant.
Stripping once at the storage boundary in _build_assistant_message() cleans the content for every downstream path in one place — no per-platform or per-path stripper needed. Measured impact on a real MiniMax M2.7-highspeed session (per @luoyejiaoe-source, #9306): 55% of assistant messages started with <think> blocks, 51/100 session titles were polluted, 16% content-size reduction.
3 new regression tests in TestBuildAssistantMessage: closed-pair strip with reasoning capture, no-think-tag passthrough, and unterminated-block strip.
Resolves#8878 and #9568.
Originally proposed as PR #9250.
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