Create an OpenAI Responses API request with custom function tools and run the tool-call loop correctly: parse function_call items, execute the tool, and submit function_call_output on the next turn

Documented steps

1. POST https://api.openai.com/v1/responses with 'Authorization: Bearer <API_KEY>', a model, an 'input', and a 'tools' array.
2. Define each tool with type:'function', name, description, a JSON-Schema 'parameters' object, and "strict": true for guaranteed schema adherence.
3. For strict mode, set additionalProperties:false on every object level and list every property of 'properties' inside 'required'.
4. Model logically-optional fields as nullable unions such as {"type":["string","null"]} rather than omitting them from required, which strict mode disallows.
5. Send the request and scan the response's 'output' array for items with type 'function_call'.
6. Read call_id, name, and arguments from each function_call item. 'arguments' is a JSON-encoded STRING: parse it before use.
7. Execute the corresponding local function with the parsed arguments.
8. Build the result item: {"type":"function_call_output","call_id":"<same call_id>","output":"<string result>"}. The output is consumed as text, so stringify JSON, error codes, or plain text.
9. Send the next POST to /v1/responses, either passing previous_response_id plus the function_call_output item, or replaying the original function_call item(s) and your output item(s) in the input array.
10. Read the model's final answer from output_text or the message-type item in output.
11. Set parallel_tool_calls:false if you need to force at most one tool call per turn.
12. Loop the call -> function_call -> function_call_output cycle until a response contains no further function_call items.