In triangle $ABC$, given $AB = 2$, $AC = 1 + \sqrt{5}$, and $\angle CAB = 54^{\circ}$. Suppose $D$ lies on the extension of $AC$ through $C$ such that $CD = \sqrt{5} - 1$. If $M$ is the midpoint of $BD$, determine the measure of $\angle ACM$ in degrees.

Let's think step by step and output the final answer within \boxed{}.
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