Trustworthy biomedical AI requires reliable action selection when evidence is missing, stale, conflicting, or late, not only accurate answers on static inputs. We instantiate an episode-level evaluation protocol as 400 synthetic healthcare workflow episodes: 40 hand-authored semantic seeds across four task classes, two surface parameterizations, and five controlled variants, scored on ANSWER/ASK CLARIFICATION/ABSTAIN/ESCALATE under a pre-declared 5:1 missed-versus-unnecessary escalation cost. Reference actions are single-author study-policy labels, not clinician-adjudicated ground truth. Across five open-weight configurations (1.7B--9.7B), clean decision accuracy reaches 0.97, yet uncertainty-prompted models miss 32--97% of required escalations. The stronger 9.7B configuration narrows but does not remove the gap, falling from 0.97 clean accuracy to 0.78 under conflict. Verbalized confidence is inconsistent (ECE 0.10--0.54; failure AUROC 0.48--0.77), and a development-tuned confidence-only policy yields no utility gain. A transparent workflow-aware controller improves 5:1 utility for every model and reduces missed escalations to 0.12--0.24, at specificity 0.83--0.93. However, a 30-concept lexical stress test reduces each rule detector's recall from 1.00 on trigger phrases to 0.00 on unseen paraphrases, limiting the controller claim to this benchmark. Seed-clustered statistics, ablations, cross-task transfer, raw outputs, and manifests are packaged for audit. The results motivate explicit workflow-state evaluation while showing that apparently effective routing controls need their own generalization tests.
Interactive tasks such as eliciting a user's preferences or diagnosing a hidden mechanism require an agent to track its uncertainty over a latent state, ask informative questions and act on the answers. Language models have no explicit mechanism for this, whereas Bayesian information seeking provides one through posterior inference and expected information gain (EIG), and we ask whether it can be distilled into an 8B language model. Our teacher, a lightweight Bayesian agent with a sequential variational belief and EIG query selection, matches or approaches exact and particle references on three task families. We generate synthetic interactions with the teacher on episodes disjoint from the benchmark and fine-tune \Student{} to reproduce its queries and its belief state as a structured scratchpad. On three Multi-Turn Puzzles tasks the student raises Circuit Decoding from 0.00 to 0.93 success, lowers the normalized rank of the recommended film from 0.50 to 0.10 and cuts word guessing from 32 to 3.4 attempts, exceeding the strongest reported language models on the two comparable tasks. Exposing the belief state closes much of the gap where the decision is an implicit computation rather than a read-out of the interaction; in matched teacher contrasts, EIG supervision consistently outperforms random querying, whereas greater inference fidelity does not uniformly improve the distilled student; a 70B language-model teacher does not match the Bayesian teacher in downstream student performance, and the learned skill does not transfer to an unseen task family. Variational Bayesian information seeking can thus be amortized into a language model by transferring the belief state that drives its questions and decisions.