text: Title: [Feature]: OpenAI Response API
  Body: ### 🚀 The feature, motivation and pitch
  
  I come across this https://platform.openai.com/docs/guides/structured-outputs?api-mode=responses&example=chain-of-thought#streaming wrt to their new Response API, so we probably also want to add support in vLLM.
  
  ### Alternatives
  
  _No response_
  
  ### Additional context
  
  _No response_
  
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