feat: enhance websearch functionality with reasoning-based approach

- Changed use_websearch default from False to True for all tools
- Redesigned websearch behavior to focus on reasoning rather than direct search
- Tools now analyze when web searches would be helpful and recommend specific searches
- Updated all tool-specific websearch instructions to be more thoughtful
- Gemini will now suggest what Claude should search for and explain why

Key improvements:
- Web search is now enabled by default for better documentation awareness
- Instead of performing searches, Gemini reasons about what searches would help
- Provides specific search recommendations for Claude to execute
- More collaborative approach between Gemini and Claude

This change makes the tools more intelligent about when external information
would be valuable while keeping Claude in control of actual web searches.

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

tools/thinkdeep.py

@@ -85,7 +85,7 @@ class ThinkDeepTool(BaseTool):
                 "use_websearch": {
                     "type": "boolean",
                     "description": "Enable web search for documentation, best practices, and current information. Particularly useful for: brainstorming sessions, architectural design discussions, exploring industry best practices, working with specific frameworks/technologies, researching solutions to complex problems, or when current documentation and community insights would enhance the analysis.",
-                    "default": False,
+                    "default": True,
                 },
             },
             "required": ["current_analysis"],
@@ -155,11 +155,11 @@ class ThinkDeepTool(BaseTool):
         # Add web search instruction if enabled
         websearch_instruction = self.get_websearch_instruction(
             request.use_websearch,
-            """Specifically search for:
-- Current documentation for technologies, frameworks, or APIs being discussed
-- Similar issues and their solutions from the community
-- Best practices and recent developments
-- Official sources to verify information""",
+            """When analyzing complex problems, consider if searches for these would help:
+- Current documentation for specific technologies, frameworks, or APIs mentioned
+- Known issues, workarounds, or community solutions for similar problems
+- Recent updates, deprecations, or best practices that might affect the approach
+- Official sources to verify assumptions or clarify technical details""",
         )
 
         # Combine system prompt with context