FKMO 2016 Problem 1

In a acute triangle $\triangle ABC$ , denote $D, E$ as the foot of the perpendicular from $B$ to $AC$ and $C$ to $AB$ . Denote the reflection of $E$ with respect to $AC, BC$ as $S, T$ . The circumcircle of $\triangle CST$ hits $AC$ at point $X (\not= C)$ . Denote the circumcenter of $\triangle CST$ as $O$ . Prove that $XO \perp DE$ .