Snap Playhead to Cut?

I would like to be able to "snap to cut" along a selected track.

If I had a track like this:


... and I want to snap the playhead to the "next cut":


Is there a way to do this?

Using the < and > keys will snap by frame and adding the shift key with go to the top and tail of the entire timeline, but is there a key combination that will snap the playhead to a cut point on a selected track?

If not, there should be!