[Reasoning + Structured Output] make reasoning compatible with structured output (#12551)

Signed-off-by: Xinyuan Tong <xinyuantong.cs@gmail.com>
Co-authored-by: Xinyuan Tong <xinyuantong.cs@gmail.com>

docs/advanced_features/structured_outputs_for_reasoning_models.ipynb

@@ -360,6 +360,13 @@
     "## Native API and SGLang Runtime (SRT)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "> Note: For native API, as a work-around, you need to set `reasoning` argument to `True` to ensure the model will think before generating the structured output. It's not required for chat-completion API."
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -407,6 +414,7 @@
     "    f\"http://localhost:{port}/generate\",\n",
     "    json={\n",
     "        \"text\": text,\n",
+    "        \"reasoning\": True,\n",
     "        \"sampling_params\": {\n",
     "            \"temperature\": 0,\n",
     "            \"max_new_tokens\": 2048,\n",
@@ -454,6 +462,7 @@
     "    f\"http://localhost:{port}/generate\",\n",
     "    json={\n",
     "        \"text\": text,\n",
+    "        \"reasoning\": True,\n",
     "        \"sampling_params\": {\n",
     "            \"temperature\": 0,\n",
     "            \"max_new_tokens\": 2048,\n",
@@ -482,6 +491,7 @@
     "    f\"http://localhost:{port}/generate\",\n",
     "    json={\n",
     "        \"text\": \"Give me the information of the capital of France.\",\n",
+    "        \"reasoning\": True,\n",
     "        \"sampling_params\": {\n",
     "            \"max_new_tokens\": 2048,\n",
     "            \"temperature\": 0,\n",
@@ -519,6 +529,7 @@
     "    f\"http://localhost:{port}/generate\",\n",
     "    json={\n",
     "        \"text\": \"Paris is the capital of\",\n",
+    "        \"reasoning\": True,\n",
     "        \"sampling_params\": {\n",
     "            \"temperature\": 0,\n",
     "            \"max_new_tokens\": 2048,\n",
@@ -547,6 +558,7 @@
     ")\n",
     "payload = {\n",
     "    \"text\": text,\n",
+    "    \"reasoning\": True,\n",
     "    \"sampling_params\": {\n",
     "        \"max_new_tokens\": 2048,\n",
     "        \"structural_tag\": json.dumps(\n",