Reasoning-enabled language model agents can incur substantial computation before acting, although the reasoning needed varies across decisions. Existing stopping signals, such as confidence and intermediate-answer stability, can vary in effectiveness across reasoning models; signals obtained from hidden states or token probabilities also require internal access that may be unavailable or impractical. We introduce StreamStop, which learns model-specific stopping policies offline from prefix-level action agreement. A frozen prefix reader encodes available reasoning text for a lightweight stop head, allowing stopping without access to the reasoning model's internal signals. We construct and publicly release a dataset of agent reasoning trajectories with prefix-level action annotations. These annotations compare each prefix action with the full-reasoning reference action, enabling offline comparison of stopping rules and exact expected-return optimization of a discounted action-agreement objective. Conditioning the head on the discount factor allows the agreement-token trade-off to be adjusted at inference without retraining. In closed-loop evaluations on WebShop and ScienceWorld, StreamStop achieves higher observed success than most validation-selected fixed-budget settings while using fewer reasoning tokens than Full thinking. On WebShop with Qwen3.8-27B, it uses 42% fewer reasoning tokens per episode with similar observed task success.

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