### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

When sending a Claude Code / Anthropic Messages style request through LiteLLM with:

- `thinking: { "type": "adaptive" }` - `output_config: { "effort": "high" }`

LiteLLM returns:

`400 {"message":"adaptive thinking is not supported on this model"}`

This happens in two cases:

1. When the request is sent to `auto_router/complexity_router` 2. When the request is sent directly to `claude-sonnet-4-6`

The issue is unexpected because the downstream target model is `claude-sonnet-4-6`, which should support adaptive thinking.

I reduced the request payload to the minimum relevant fields below. The original request was generated by Claude Code / Anthropic Messages style clients and included tools/system content, but the failure appears tied to the `thinking.type=adaptive` handling rather than the full prompt contents.

### Steps to Reproduce

1. Configure LiteLLM with a router model using `auto_router/complexity_router`, with all tiers pointing to `claude-sonnet-4-6`.

Example router config: ```json { "model": "auto_router/complexity_router", …