In the tetrahedron $A B C D$ , $A D \perp C D , A D = C D$ , $\angle A D B = \angle B D C$ , and $E$ is the midpoint of $A C$.
(1) Prove: Plane $B E D \perp$ plane $A C D$ ;
(2) Given $A B = B D = 2 , \angle A C B = 60 ^ { \circ }$ , point $F$ is on $B D$ . When the area of $\triangle A F C$ is minimized, find the volume of the tetrahedron $F - A B C$ .