Read the tiny pins

Trace a pin back to the ring that owns it. That gives you a pair to inspect: the supporting ring and the ring whose gap must pass the connection. An outer piece with fewer neighbours is often easier to understand first.

A stop pin is a physical limit, not a cue to swipe harder. If the short rotation hits a stop, inspect the path in the other direction. Keep your next turn small enough to see which contact changed.

After a piece leaves, look again. The remaining network is a different puzzle, and a ring that looked trapped a moment ago may now have a clear sweep.