Analog device sizing must satisfy all specifications across process, voltage, and temperature (PVT) corners to ensure tape-out success, but simulating every candidate at all corners dominates the sizing time and slows design iteration. Conventional surrogate-based optimizers search the sizing space directly, while recent large language model (LLM) agents add circuit knowledge to designs but still delegate the sizes to global optimizers. Both learn the circuit response from repeated multi-corner SPICE simulations and optimize on top of it, which becomes expensive under a limited simulation budget. Providing an agent with reusable verified designs and sizing sub-blocks analytically could save most of this budget. We propose AnalogScout, a simulation-efficient PVT-aware sizing framework driven by an LLM agent. Combining elite-design reuse, analytic gm/Id local sizing and global refinement under full-corner verification, AnalogScout reduces power by 43.3% relative to the evolution strategy CMA-ES at an equal budget of 16k simulations on three SKY130 OTAs of increasing complexity, and reaches the final CMA-ES power after 7.0% of that budget. It also attains lower power than Bayesian optimization on all three OTAs and than two re-implemented LLM-driven flows on the two OTAs where they were tested.