HMMT 2015 G6

In triangle $A B C, A B=2, A C=1+\sqrt{5}$, and $\angle C A B=54^{\circ}$. Suppose $D$ lies on the extension of $A C$ through $C$ such that $C D=\sqrt{5}-1$. If $M$ is the midpoint of $B D$, determine the measure of $\angle A C M$, in degrees.