[responsesAPI] parse reasoning item input (#28248)

Signed-off-by: Andrew Xia <axia@fb.com>
Co-authored-by: Andrew Xia <axia@fb.com>
Co-authored-by: Cyrus Leung <tlleungac@connect.ust.hk>

examples/online_serving/openai_responses_client.py

@@ -0,0 +1,44 @@
+# SPDX-License-Identifier: Apache-2.0
+# SPDX-FileCopyrightText: Copyright contributors to the vLLM project
+"""
+Set up this example by starting a vLLM OpenAI-compatible server.
+Reasoning models can be used through the Responses API as seen here
+https://platform.openai.com/docs/api-reference/responses
+For example:
+vllm serve Qwen/Qwen3-8B --reasoning-parser qwen3
+
+"""
+
+from openai import OpenAI
+
+input_messages = [{"role": "user", "content": "What model are you?"}]
+
+
+def main():
+    base_url = "http://localhost:8000/v1"
+    client = OpenAI(base_url=base_url, api_key="empty")
+    model = "Qwen/Qwen3-8B"  # get_first_model(client)
+    response = client.responses.create(
+        model=model,
+        input=input_messages,
+    )
+
+    for message in response.output:
+        if message.type == "reasoning":
+            # append reasoning message
+            input_messages.append(message)
+
+    response_2 = client.responses.create(
+        model=model,
+        input=input_messages,
+    )
+    print(response_2.output_text)
+    # I am Qwen, a large language model developed by Alibaba Cloud.
+    # I am designed to assist with a wide range of tasks, including
+    # answering questions, creating content, coding, and engaging in
+    # conversations. I can help with various topics and provide
+    # information or support in multiple languages. How can I assist you today?
+
+
+if __name__ == "__main__":
+    main()