Endgame king activity and passed pawns: march the king, push the passer

With the queens off, the king is a strong piece — walk it towards the middle. Once the queens come off, start every plan with "where does my king belong?"

A passed pawn is a threat only if it moves — and a rook belongs behind it. With a passed pawn, every plan starts with "how does this pawn get another square?"

The board defines the opportunity — a position where the principle applies — and Stockfish is the referee: a miss is counted only when the engine’s own line at that move embodies the principle, so the row never blames you for a rule the position did not ask for. The row reads as tests passed out of tests taken.