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Reasoning models think more deeply before answering — good for math, code, and multi-step tasks. Use reasoning_effort to control depth (e.g. low / medium / high).
curl https://tokendog.io/v1/chat/completions \
  -H "Authorization: Bearer $TOKENDOG_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "model":"gpt-5.1",
    "reasoning_effort":"high",
    "messages":[{"role":"user","content":"A number plus half of itself equals 36. Find the number."}]
  }'
Higher effort means deeper thinking but more latency and cost; use low for simple tasks.