Reading this maze
Crossing the atrium starts at row 5, column 4. Of the 42 grid positions, 30 are paintable and 12 are walls. The start is already painted; the other 29 tiles remain to be reached.
Diamond A at row 5, column 6 toggles both barred cells marked A. Diamond B at row 1, column 3 toggles the gate marked B. Start up and stop at row 4, column 4. Both A gates share one state, while B stays independent; plan the closed bars as stopping points. The first slide covers 2 of 30 target tiles.
The verified opening crosses 1 tiles before stopping. A breadth-first search proves a 29-slide finish from this exact starting board; that is a reference target, not a move limit. You may revisit any painted tile.
A and B keep separate states. The A diamond toggles both A gates together, while the B diamond toggles only B. Every barred cell must be painted. Undo restores all gate states, and Hint searches your current trail.