Proof Writing & Problem Solving · Medium problem

Four numbers stand around a circle: $1, 5, 11, 20$. One step replaces every number, all at once, by the absolute difference between it and its clockwise neighbour, so $(a, b, c, d)$ becomes $(|a - b|, |b - c|, |c - d|, |d - a|)$. After how many steps are all four numbers $0$ for the first time?