HMMT November 2014 T10

Let $A B C D E F$ be a convex hexagon with the following properties. (a) $\overline{A C}$ and $\overline{A E}$ trisect $\angle B A F$. (b) $\overline{B E} \| \overline{C D}$ and $\overline{C F} \| \overline{D E}$. (c) $A B=2 A C=4 A E=8 A F$.

Suppose that quadrilaterals $A C D E$ and $A D E F$ have area 2014 and 1400, respectively. Find the area of quadrilateral $A B C D$.