text: Title: [Feature]: Support openai responses API interface
  Body: ### 🚀 The feature, motivation and pitch
  
  OpenAI has released a new Responses API, but vLLM does not currently support it. 
  We request that vLLM adds compatibility with this API to stay in sync with OpenAI's updates. 
  Supporting the Responses API will enhance vLLM's utility and competitiveness. 
  For more details, see the OpenAI documentation
  
  * OpenAI Responses api reference
    https://platform.openai.com/docs/api-reference/responses
  
  * OpenAI Responses vs. Chat Completions
  https://platform.openai.com/docs/guides/responses-vs-chat-completions
  
  ### Alternatives
  
  _No response_
  
  ### Additional context
  
  _No response_
  
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