docs: add mcp_config example with sequential-thinking server

- Add mcp_config to inputs table
- Add example section showing how to use mcp_config with sequential-thinking MCP server
- Include clear explanation that custom servers override built-in servers

Co-authored-by: ashwin-ant <ashwin-ant@users.noreply.github.com>

README.md

@@ -82,6 +82,7 @@ jobs:
 | `allowed_tools`       | Additional tools for Claude to use (the base GitHub tools will always be included)                                   | No       | ""        |
 | `disallowed_tools`    | Tools that Claude should never use                                                                                   | No       | ""        |
 | `custom_instructions` | Additional custom instructions to include in the prompt for Claude                                                   | No       | ""        |
+| `mcp_config`          | Additional MCP configuration (JSON string) that merges with the built-in GitHub MCP servers                          | No       | ""        |
 | `assignee_trigger`    | The assignee username that triggers the action (e.g. @claude). Only used for issue assignment                        | No       | -         |
 | `trigger_phrase`      | The trigger phrase to look for in comments, issue/PR bodies, and issue titles                                        | No       | `@claude` |
 
@@ -89,6 +90,33 @@ jobs:
 
 > **Note**: This action is currently in beta. Features and APIs may change as we continue to improve the integration.
 
+### Using Custom MCP Configuration
+
+The `mcp_config` input allows you to add custom MCP (Model Context Protocol) servers to extend Claude's capabilities. These servers merge with the built-in GitHub MCP servers.
+
+Example: Adding a sequential thinking server:
+
+```yaml
+- uses: anthropics/claude-code-action@beta
+  with:
+    anthropic_api_key: ${{ secrets.ANTHROPIC_API_KEY }}
+    mcp_config: |
+      {
+        "mcpServers": {
+          "sequential-thinking": {
+            "command": "npx",
+            "args": [
+              "-y",
+              "@modelcontextprotocol/server-sequential-thinking"
+            ]
+          }
+        }
+      }
+    # ... other inputs
+```
+
+This configuration adds the sequential thinking MCP server, which provides Claude with enhanced problem-solving capabilities. Your custom servers will override any built-in servers with the same name.
+
 ## Examples
 
 ### Ways to Tag @claude