BALKAN-SL 2021 G5

Let $A B C$ be an acute triangle with $A C>A B$ and circumcircle $\Gamma$. The tangent from $A$ to $\Gamma$ intersects $B C$ at $T$. Let $M$ be the midpoint of $B C$ and let $R$ be the reflection of $A$ in $B$. Let $S$ be a point so that $S A B T$ is a parallelogram and finally let $P$ be a point on line $S B$ such that $M P$ is parallel to $A B$.

Given that $P$ lies on $\Gamma$, prove that the circumcircle of $\triangle S T R$ is tangent to line $A C$.