Full-duplex dialogue requires timely yet selective interruption handling, which end-of-turn prediction alone cannot achieve: complete utterances may need no response, while unfinished requests may warrant interruption. To address this challenge, we propose HiThink Turn, an intent-aware streaming turn-state predictor that separates response intent from semantic completeness and conditions decisions on system playback state. A key contribution is minimal intent-sufficient prefix supervision, constructed through LLM judgments and speech alignment, while training on audio truncated at chunk boundaries improves robustness to partial speech. These components support streaming inference with 240-ms audio chunks, enabling low-latency, accurate full-duplex turn control. Experiments show that HiThink Turn leads the compared methods in Easy Turn macro accuracy, Full-Duplex-Bench average interaction rate score (0.933), and non-target-speech average playback resume rate (0.735). Additionally, intent-prefix triggering raises interruption success from 89\% to 98\% and reduces mean stop latency by 60.9\%.

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