Let A B C be a triangle. Points D and E are placed on \overline{A C} in the order A, D, E, and C, and point F lies on \overline{A B} with E F \| B C. Line segments \overline{B D} and \overline{E F} meet at X. If A D=1, D E=3, E C=5, and E F=4, compute F X.