Humans are also incapable of knowing whether their output is correct. We merely convince ourselves that it is and then put our thoughts in contact with the external world and other people to see if we actually are.

So then we are capable of knowing whether our output is correct, by putting it into contact with the external world.

Humans are capable of using formal logic to reach a provably correct conclusion from valid premises. That conclusion can then be used as premises for a further conclusion. Follow the logic the other way and using our powers of observation, and sensing, we can gather base level truths and know that what we are saying is correct in an absolute sense.

Computers use formal logic all the time to output truth, LLMs, however, do not.