Why do I need a source? An LLM prompt does not "move to action", because an LLM does not act. People act, animals act, software doesn't act. Acting implies volition and volition implies cognition and if you think that LLMs have those things then you're the one who should provide a source for your claim.
How about an LLM connected to a robotic arm. What then?
As for cognition - can you prove that you possess it, to an external observer? Could you, confined to a box through which you can only communicate through textual messages, prove that you are thinking, and not just responding through a mechanistic process?