Restricted Move Set Cube Solver

Enter a 3×3 scramble in standard WCA notation. This solves it with Kociemba's two-phase algorithm, then rewrites the solution using only four allowed actions: x (rotate cube like R), y (rotate cube like U), R (twist right face CW), U (twist top face CW) — no counterclockwise or half-turn variants. Since a counterclockwise turn costs 3 actions here, it also searches a few shorter alternate solver solutions in the background and keeps whichever converts to the fewest total actions.