Olympiad Geometry · Superchallenge problem

In $\triangle ABC$, point $D$ lies on $\overline{AB}$ and point $E$ lies on $\overline{AC}$ with $\overline{DE} \parallel \overline{BC}$. Segments $\overline{BE}$ and $\overline{CD}$ meet at $P$. Triangle $PDE$ has area $4$ and triangle $PBC$ has area $25$. Find the area of $\triangle ABC$.