<image>As shown in the figure, in the right triangular prism ABC-A_{1}B_{1}C_{1}, E and F are the midpoints of A_{1}B and A_{1}C respectively, and point D is on B_{1}C_{1}. A_{1}D is perpendicular to B_{1}C. Prove that:
(1) EF is parallel to plane ABC;
(2) Plane A_{1}FD is perpendicular to plane BB_{1}C_{1}C.

