如图,在平面四边形$ABCD$中,$AD=1,CD=2,AC=\sqrt{7}$.
(1)求$\cos \angle CAD$的值;
(2)若$\cos \angle BAD=-\frac{\sqrt{7}}{14}$,$\sin \angle CBA=\frac{\sqrt{21}}{6}$,求$BC$的长.