Search the models available to Agent Manager sessions and inspect their reasoning variants.

Use this tool before `agent_manager` when you need to pick a model or reasoning effort. Results are grouped by model, not by provider, and list every provider that offers each model so you can constrain the provider when needed. With no arguments it returns the top available models (capped at 20); pass `query` to search by model name or ID, and `offset` to page further. The query is matched leniently: it is case-insensitive, ignores spacing and punctuation, and is order-independent, so `opus claude`, `glm5.2`, and `gpt5` all work. You do not need the exact model name.

Each result includes the model name, its reasoning variant names, and the providers that offer it. Pass the model name back as the `agent_manager` task `model`; pass one of the listed provider IDs as the task `provider` when the provider must be explicit. When `provider` is omitted, Agent Manager resolves it automatically, preferring the one used by the current turn and falling back to the Kilo Gateway.
