Triangle $ABC$ has $AB=32$, $BC=8$ and $AC=8\sqrt{17}$. Let $P$ be the point on $\overline{AC}$ such that $PC=2\sqrt{17}$. There are exactly two points $D$ and $E$ on line $BP$ such that quadrilaterals $ABCD$ (with $AD\parallel BC$) and $ABCE$ (with $CE\parallel AB$) are trapezoids. What is the distance $DE$?