I built an assistant in Vapi, which I want to integrate as a chatbot, and I want the bot to respond by actually performing a web search, but it doesn't. Can you please tell me which LLM can do that for me? Many LLMs don't offer web search through APIs.

I recommend you to use a custom tool where you perform the search

Use an LLM that supports real-time search like Claude 3, then connect it using Vapi’s function-calling to fetch and respond with live web data..