> Are LLMs trained to do all that

Yes, they are trained to do all that more or less as much as anything else they are trained to do.

> How do you know they cannot?

The same way I know they can't run a fortune 500 company. It's clearly apparent.

Last time I checked they were trained to predict the next word. Why would you expect them to solve research problems?

> Why would you expect them to solve research problems?

I don't.

Great, then we established that I (generally intelligent human), and LLMs, both can't perform the task in question without specific training. We still don't know if given that specific training we (a specific human or a specific LLM) would be able to perform it.