How do I cross the first gap in the cliff?

Hint 1 of 5:

You're not going to be able to cross by going "east" (to the right).

Hint 2 of 5:

You'll have to climb up to the top.

Hint 3 of 5:

Perhaps a tool is needed to climb to the top.

Hint 4 of 5:

Did you remember to save the rope from your stay at the inn?