Order the lifecycle of a single extended thinking API call

An extended-thinking call has a clean five-step lifecycle that every major reasoning provider follows. **Step 1: client sends the prompt with a thinking budget.** This can be an explicit token cap, an effort level (low / medium / high), or a feature flag enabling thinking. The choice tells the model how much hidden reasoning to spend. **Step 2: the model generates reasoning tokens.** Before producing the visible answer, the model emits a chain of internal thinking tokens. The trace can be a few hundred tokens on an easy prompt or many thousands on a hard one. **Step 3: the provider hides or summarizes the trace.** What returns over the wire is either a summarized version, a fully redacted placeholder, or nothing at all depending on the provider. The raw chain of thought is generally not exposed. **Step 4: visible answer tokens stream back.** Now the model emits the final answer, which is what the user sees and what your application parses. **Step 5: usage metadata reports the bill.** The response object includes a reasoning_tokens count alongside output_tokens, and the reasoning portion bills at the output rate. This is where you discover how much the hidden trace cost.

**Budget in, think, hide, answer, bill.** That is the lifecycle of an extended-thinking call. The client attaches a thinking budget or effort setting to the request. The model then runs an internal reasoning trace before committing to a final answer. The provider applies a privacy or product policy to the trace, returning either a summary, a redacted placeholder, or nothing at all; the raw chain of thought is almost never exposed verbatim. Once thinking concludes, visible answer tokens stream back to the client. The response object reports usage metadata with a separate reasoning_tokens count that bills at the output rate. **Why this ordering matters in production.** Because thinking and visible tokens share one completion window, a `max_tokens` set below the thinking budget truncates step 2 and step 4 never happens. Because the provider hides step 3, you cannot debug a wrong answer by reading the trace; you have to rely on probes, ablations, and prompt experiments. Because the bill is determined in step 5, your cost dashboards must read reasoning_tokens separately from output_tokens or you will misattribute spend. Each step has an operational consequence that lives downstream of the lifecycle itself.