OpenAI Reasoning Tokens: Budget for Invisible Thinking

During its thinking phase, an o-series model explores branches, backtracks from contradictions, and verifies conclusions using hidden reasoning tokens that are never exposed in the UI but are billed and count toward context budgets and tokens-per-minute (TPM) rate limits. Always leave generous max_output_tokens headroom for hidden reasoning tokens while requesting a concise visible answer in the prompt text.

API Config: Allocate sufficient max_output_tokens headroom for invisible thinking tokens. Prompt: Solve the scheduling constraint satisfaction problem below. Present only the final validated timetable in your visible response.