What happens to an LLM agent's tool choice when the reliable tool silently changes within an ongoing session? We borrow the notion of set-shifting from cognitive psychology to study how well agents adapt to hidden reliability shifts. Our cognitive test for LLM agents mounts libraries of redundant tools and skills, in which many tools solve the same task but differ in hidden reliability. Using a branching schedule, we shift the reliable tool group in the environment and compare it with a stable control, allowing us to isolate the effect of each shift on the agent's behavior. We conduct our study on a panel of LLMs equipped with harnesses and show that the same set of shifts results in distinct behaviors across models: some latch onto a fixed routine within a few turns, whereas others continue to vary. Less capable models often omit the reliable tool group, while frontier models keep calling it alongside the other groups. We introduce a suite of measures to quantify agent behavior after reliability shifts. While policy prompting substantially alters behavior in some tested models, our findings highlight agents' brittleness when changes occur in indirectly observable context.

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