Current multimodal large language models (MLLMs) suffer from unstable reasoning due to the lack of mechanisms for controlling reasoning trajectories, often leading to hallucinated conclusions. Our analysis reveals that early-stage uncertainty induces trajectory switching, significantly increasing hallucination risk. We propose MedMMV, an evidence-grounded trajectory control framework that treats reasoning as a search-and-selection process over candidate trajectories. By constructing, refining, and selecting among multiple reasoning paths, MedMMV improves reliability and produces structured supervision signals over trajectory quality. We further convert these signals into learnable objectives for post-training, including reject sampling and pairwise preference learning, enabling smaller models to learn trajectory selection as an efficient single-pass capability. Instead of merely imitating reasoning traces, the model is trained to assign higher likelihood to preferred trajectories. Experiments show that richer supervision leads to stronger transfer, with accuracy improving from 10.5% to 29.0%. Our results demonstrate that trajectory selection is the key transferable capability for reliable reasoning.

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