Puzzletober 2024: Roam

Right in front of me is the highest point on this square-shaped island, but the cliff looks too steep to ascend, so I'll have to go south. It's unclear at the moment exactly how I want to approach getting there, so I'll have to trust that, from here on out, there's a way I can cover the whole area without retracing my steps instead of having to roam senselessly.

The rules to this puzzle are meant to be deduced. The answer is a path.

penpa link