> the unique event will be the AI having the ability to act on its own without a "prompt"

That's super easy. The reason they need a prompt is that this is the way we make them useful. We don't need LLMs to generate an endless stream of random "thoughts" otherwise, but if you really wanted to, just hook one up to a webcam and microphone stream in a loop and provide it some storage for "memories".

And the ability to improve itself.