What Exactly Defines an AI Agent?

I’m working on an AI/ML project that integrates external tools for planning, memory, execution, and prewritten commands. I’d like a clear, concise definition of an AI agent. Does simply giving an LLM access to tools qualify it as an agent? For instance, ChatGPT has a built-in search feature—does that alone make it an AI agent? Do AI agents require explicit goals or objectives? I want to know if my current implementation meets the formal criteria of an AI agent.

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