2016 AIME I Problem 6

In \triangle A B C let I be the center of the inscribed circle, and let the bisector of \angle A C B intersect \overline{A B} at L. The line through C and L intersects the circumscribed circle of \triangle A B C at the two points C and D. If L I=2 and L D=3, then I C=\frac{p}{q}, where p and q are relatively prime positive integers. Find p+q.