SHARYGIN 2021 Problem 83

Three cockroaches run along a circle in the same direction. They start simultaneously from a point $S$ . Cockroach $A$ runs twice as slow than $B$ , and thee times as slow than $C$ . Points $X, Y$ on segment $SC$ are such that $SX = XY =YC$ . The lines $AX$ and $BY$ meet at point $Z$ . Find the locus of centroids of triangles $ZAB$ .