OLYMPIC-REVENGE 2021 Problem 3

Let $I, C, \omega$ and $\Omega$ be the incenter, circumcenter, incircle and circumcircle, respectively, of the scalene triangle $XYZ$ with $XZ > YZ > XY$ . The incircle $\omega$ is tangent to the sides $YZ, XZ$ and $XY$ at the points $D, E$ and $F$ . Let $S$ be the point on $\Omega$ such that $XS, CI$ and $YZ$ are concurrent. Let $(XEF) \cap \Omega = R$ , $(RSD) \cap (XEF) = U$ , $SU \cap CI = N$ , $EF \cap YZ = A$ , $EF \cap CI = T$ and $XU \cap YZ = O$ .

Prove that $NARUTO$ is cyclic.