I think the reason for the common lingual similarity in treating problems and tasks is the ACTUAL similarity. Could-ness, or reachability of a theoretical (alternate past or unknown future) world-state is not binary. It's a probability function related to likelihood of theoretical actions and likelihood of various results of those actions.

If your could-ness function returns one bit of information, it's too simple to be very useful. And any theory of decision-making based on it is equally oversimplified.

I do think there's value in exploring this as a (false, but perhaps novel) quantization. Choosing between physical movement vs searching for alternate plans vs abandoning/altering goals (all of which are action, but feel somewhat different) is a real part of any decision theory.

I don't think the quantization is real. The chose of what to do next (perform some physical action, think about alternate strategies, or rethink goals (or change focus to a different goal)) is valid and necessary for things labeled tasks as well as those labeled problems.