### Summary

`/health` reports a model in `unhealthy_endpoints` with `BadRequestError: Could not finish the message because max_tokens or model output limit was reached`, even though the same model returns valid completions on `/v1/chat/completions` immediately after.

### Root cause

The internal health-check probes with `max_tokens: 1` regardless of the per-model `max_tokens` set in `model_list`. For reasoning models (gpt-5.5, deepseek-v4-pro, grok-4.20-reasoning, sonnet-4-5-thinking with extended thinking, etc.) the model spends reasoning tokens before producing visible output. With `max_tokens=1`, the model exhausts its budget on internal reasoning and returns the BadRequestError above.

### Reproduction (LiteLLM proxy v1.x, latest as of 2026-04-30)

`config.yaml`: ```yaml model_list: - model_name: gpt-5.5 litellm_params: model: gpt-5.5 api_key: os.environ/OPENAI_API_KEY max_tokens: 16384 timeout: 240 ```

```bash curl -H "Authorization: Bearer $LITELLM_MASTER_KEY" http://localhost:4000/health # → unhealthy_endpoints[gpt-5.5]: "Could not finish the message because max_tokens or model output limit was reached"

curl -H "Authorization: Bearer $LITELLM_MASTER_KEY…