Let \( H \) be the orthocenter, and \( O \) be the circumcenter of \( \triangle ABC \). The line \( AH \) intersects the circumcircle of \( \triangle ABC \) at point \( N \) for the second time. The circumcircle of \( \triangle BOC \), with center at point \( Q \), intersects the line \( OH \) at point \( X \) for the second time. Prove that the points \( O, Q, N, X \) lie on the same circle. Proposed by Matthew Kurskyi