tavily-ai/convex-tavily ? reverse-engineered prompt

Build me a small Convex component for using Tavily in a Convex app.

I want it to let an app call a typed client for web search and page extraction, while keeping the Tavily API key in Convex env config. The app should use its own action as the wrapper, so I can add auth, rate limiting, or other checks there before calling the Tavily component.

Please include a simple example showing how to configure the component, set the TAVILY_API_KEY, and call search and extract from an action. Search should support a few useful options like advanced search and returning a small set of results, and extract should handle a list of URLs and optional query focused extraction. Keep it stateless, with no database tables.

If you need to check the latest Convex or Tavily docs while building it, go ahead and look them up.