Contextual automatic speech recognition (ASR) improves rare-entity recognition by supplying candidate hotwords, but retrieved candidates may be incomplete or incorrect. A reliable system must therefore exploit a relevant candidate without allowing unsupported alternatives to override the acoustic evidence. We propose a context-steered reasoning framework that generates a short, audio-grounded caption before transcription. This task-specific representation lets the model assess candidate relevance before making a lexical decision. Supervised fine-tuning establishes the structured caption-to-transcription behavior, while targeted trajectory injection strengthens group relative policy optimization when difficult utterances yield only unsuccessful rollouts. Experiments across diverse context conditions show that the proposed method consistently improves both transcription quality and hotword recognition while remaining robust to irrelevant candidates.

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