In triangle ABC, $\angle \mathrm { A } = \frac { \pi } { 3 }$ and $\overline { \mathrm { AB } } : \overline { \mathrm { AC } } = 3 : 1$. If the circumradius of triangle ABC is 7, let $k$ be the length of segment AC. Find the value of $k ^ { 2 }$. [4 points]