Let $ABCD$ be a tetrahedron and $M$ and $N$ be the midpoints of $AC$ and $BD$, respectively. Show that for every point $P \in (MN)$ with $P \neq M$ and $P \neq N$, there exist unique points $X$ and $Y$ on segments $AB$ and $CD$, respectively, such that $X,P,Y$ are collinear.