In triangle $ABC$, $AB = 10$, $BC = 12$, and $AC = 14$. The angle bisector of $\angle BAC$ intersects $BC$ at $D$. The segments $AD$, $BD$, and $DC$ divide the triangle into two smaller triangles, $\triangle ABD$ and $\triangle ACD$. If the area of $\triangle ABC$ is 60 square units, find the ratio of the area of $\triangle ABD$ to the area of $\triangle ACD$. Let's think step by step and output the final answer within \boxed{}.
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