In an isosceles trapezoid $A B C D$, $A B=C D=3$, the base $A D=7, \angle B A D=60^{\circ}$. On the diagonal $B D$ there is a point $M$ such that $B M: M D=3: 5$.

Which side of the trapezoid, $B C$ or $C D$, does the extension of segment $A M$ intersect?