Let $ABC$ be a triangle with circumcenter $O$ and incenter $I$, ex-center in angle $A$ is $J$. Denote $D$ as the tangent point of $(I)$ on $BC$ and the angle bisector of angle $A$ cuts $BC$, $(O)$ respectively at $E, F$. The circle $(DEF )$ meets $(O)$ again at $T$. Prove that $AT$ passes through an intersection of $(J)$ and $(DEF )$.