Question 85
Let $ABC$ be a triangle of area $1$ (square units), and let $P$ denote the midpoint of the side $BC$. Consider two points $M$ and $N$ interior to the sides $AB$ and $AC$ respectively, such that $|AM| = 2|MB|$ and $|CN| = 2|AN|$. The lines $AP$ and $MN$ intersect at a point $D$. Find the area of the triangle $ADN$.