docs: add agentic loop hook guide

docs/my-website/docs/proxy/agentic_loop_hook.md

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+# Agentic Loop Hook
+
+Build a `CustomLogger` callback that intercepts a model response, fulfills tool calls server-side, and reruns the model — transparently to the caller.
+
+:::info Supported call types
+- `async` only (sync calls do not trigger the hook)
+- Non-streaming only (streaming responses cannot be inspected for tool calls)
+- Works on both `/v1/messages` and `/v1/chat/completions`
+:::
+
+## Implement the callback
+
+Override two methods on `CustomLogger`:
+
+```python
+from litellm.integrations.custom_logger import CustomLogger
+from litellm.types.integrations.custom_logger import AgenticLoopPlan, AgenticLoopRequestPatch
+
+MY_TOOL = "my_tool"
+
+class MyToolCallback(CustomLogger):
+
+    async def async_should_run_agentic_loop(
+        self, response, model, messages, tools, stream, custom_llm_provider, kwargs
+    ):
+        # Return (True, context_dict) if there are tool calls to handle
+        content = getattr(response, "content", None) or []
+        calls = [b for b in content if isinstance(b, dict)
+                 and b.get("type") == "tool_use" and b.get("name") == MY_TOOL]
+        if not calls:
+            return False, {}
+        return True, {"tool_calls": calls}
+
+    async def async_build_agentic_loop_plan(
+        self, tools, model, messages, response,
+        anthropic_messages_provider_config,
+        anthropic_messages_optional_request_params,
+        logging_obj, stream, kwargs,
+    ):
+        calls = tools["tool_calls"]
+        results = [f"result for {c['input']}" for c in calls]  # your logic here
+
+        follow_up = messages + [
+            {"role": "assistant", "content": [
+                {"type": "tool_use", "id": c["id"], "name": c["name"], "input": c["input"]}
+                for c in calls
+            ]},
+            {"role": "user", "content": [
+                {"type": "tool_result", "tool_use_id": c["id"], "content": results[i]}
+                for i, c in enumerate(calls)
+            ]},
+        ]
+        return AgenticLoopPlan(
+            run_agentic_loop=True,
+            request_patch=AgenticLoopRequestPatch(messages=follow_up),
+        )
+```
+
+For `/v1/chat/completions`, override `async_build_chat_completion_agentic_loop_plan` instead — same idea, `optional_params` replaces `anthropic_messages_optional_request_params`.
+
+## Register it
+
+```python
+import litellm
+litellm.callbacks = [MyToolCallback()]
+```
+
+Or in `config.yaml`:
+
+```yaml
+litellm_settings:
+  callbacks: ["my_module.MyToolCallback"]
+```
+
+## `AgenticLoopPlan` fields
+
+| Field | Effect |
+|---|---|
+| `run_agentic_loop=True` + `request_patch` | Reruns the model with the patched request |
+| `response_override` | Returns this value directly to the caller (no rerun) |
+| `terminate=True` | Stops the loop, returns the current response |
+| `run_agentic_loop=False` (default) | Skips; next callback is checked |
+
+`AgenticLoopRequestPatch` accepts: `model`, `messages`, `tools`, `max_tokens`, `optional_params`, `kwargs`.
+
+## Loop safety
+
+- Default max reruns: `3` — override per-request with `kwargs["max_agentic_loops"]`
+- Identical tool-call fingerprints abort the loop automatically
+- Current depth is in `kwargs["_agentic_loop_depth"]`
+
+## Examples in this repo
+
+- `litellm/integrations/compression_interception/handler.py`
+- `litellm/integrations/websearch_interception/handler.py`