(12 points)
As shown in the figure, in the pyramid $P$-$ABCD$, the base face $PAD$ is an equilateral triangle, $\angle BAD = \angle ADC = 90°$.
(1) Prove that the plane $PAD$ is perpendicular to the base $ABCD$ (or a related perpendicularity result).
(2) If the area of $\triangle PCD$ is $2\sqrt{7}$, find the volume of pyramid $P$-$ABCD$.