Well the problem is it not having any reasoning period.
Not clear what symbolic reasoning would entail, but puzzles generally require you to think through several approaches to solve them, too. That requires a world model, a search, etc. the kind of stuff that actual AIs, even a tik tac toe AI, have, but LLMs don't.
On top of it this all works through machine learning, which produces the resulting network weights through very gradual improvement at next word prediction, tiny step by tiny step. Even if some sort of discrete model (like say the account of what's on either side of the river) could help it predict the next token, there isn't a tiny fraction of a discrete "model" that would help it, and so it simply does not go down that path at all.
Well I'll be damned, they are trying to get it to work as if it had internal state, by augmenting their training dataset with some auto-generated crap. Of course, if machine learning wasn't shit at recurrence they wouldn't be using transformer architecture, so it doesn't work.
I got the following from chatgpt:
By following this sequence, Janet successfully transports all 3 ducks and all 3 eggs across the river in 13 trips. Each trip involves either transporting one duck or one egg, adhering to the constraint that Janet can only carry one item (duck or egg) with her in the boat.