RS-SMO 2022 Problem 1

Let $k$ be incircle of acute triangle $ABC$ , $AC\neq BC$ , and $l$ be excircle that touches $AB$ . Line $p$ through the $C$ is orthogonal to $AB$ , $p\cap k = \{X, Y\}$ , $p\cap l = \{Z, T\}$ and the point arrangement is $X-Y-Z-T$ . Circle $m$ through $X$ and $Z$ intersects $AB$ at $D$ and $E$ . Prove that points $D,Y,E,T$ are concyclic.