+357 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 $AN = MC = 13$ and $MN = 8$, and $\overline{AN}$ and $\overline{CM}$ intersect at $X$, then what is $AX$?
