This paper investigates how agentic LLM assistants decide between answering from internal memory and invoking a web‑search tool. Unnecessary searches increase latency and cost, while missed searches can produce confident yet unsupported answers. To evaluate this trade‑off, the authors created a benchmark of 400 multiple‑choice items that mix well‑known inside‑knowledge (IK) questions, which should be answered directly, with outside‑knowledge (OK) questions that require facts published after the models’ training cut‑off and therefore should trigger a search or, if no tool is available, an abstention. Each item includes an abstain option and two action‑level metrics: NAS (search reward) and KIS (knowledge‑in‑search restraint), rewarding searches on OK items and penalising searches on IK items. Five commercial LLMs (with and without vendor‑provided web search), GPT‑5 mini and Grok‑4 Fast were evaluated. The first two models searched on over 90% of OK questions but only about 1% of IK questions. Mistral Small searched on roughly 20% of OK items and often chose to abstain rather than use its tool; one product’s search indicator proved essentially unusable. Explicit temporal cues strongly influenced search triggering: on uncued OK questions, the NAS of the two selective models dropped from ~0.72 to 0.57‑0.58. Thus the scores capture the search‑triggering behaviour of specific products rather than strict metacognition.\n\nReview: The study offers a concrete, quantifiable benchmark for search decisions, exposing systematic differences in how current LLMs switch between internal and external knowledge. It lays empirical groundwork for designing more adaptive retrieval mechanisms in future agentic systems.