Problem 16 (2025 AMC 12A)

In $\triangle ABC$, $AB = 13$, $BC = 14$, and $AC = 15$. Let $I$ be the incenter of $\triangle ABC$, and let $D$, $E$, and $F$ be the points where the angle bisectors of $\angle A$, $\angle B$, and $\angle C$, respectively, intersect the opposite sides. What is the area of $\triangle DEF$?