In $\triangle ABC$, $AB=AC=10$ and $BC=12$. Let $D$ be a point on side $BC$ such that $\overline{AD}$ bisects $\angle BAC$. The locus of all points $P$ such that the sum of the distances from $P$ to $B$ and $P$ to $C$ is constant forms an ellipse. Find the length of the major axis of this ellipse. Let's think step by step and output the final answer within \boxed{}.
user