Geometry

In triangle $ABC$, let $M$ be the midpoint of $\overline{AB}$ and $N$ be on $\overline{BC}$ such that $\overline{AN}$ is an altitude of $\triangle ABC$.  If $AB = AC = 4$ and $BC = 2$, and $\overline{AN}$ and $\overline{CM}$ intersect at $X$, then what is $AX$?