2D topdown generating stairs (access) to generated hill

Hey, I'm doing 2d topdown procedurally generated world. I'm generating perlin height values, and when certain value is crossed I'm generating one level higher, while edging biomes creates cliff of the mountain. Cliffs cannot be crossed so now I'm curious how would I do access to the generated mountain. I've got stairs tiles but I need help finding proper way of finding correct place on the mountain to actually generate them.

This is what mountain could look like :

Obviously stairs can be generated only on places where mountain is facing down(where the cliff is). I'm not sure when is ideal time to actually do this. During generating perlin or when rendering cliff(but then there is problem to find correct spot in the mountain to generate them. Also There should be only some stairs in the mountain not in every single cliff facing down.