Let A B C D be a unit square, and suppose that E and F are on \overline{A D} and \overline{A B} such that A E=A F=\frac{2}{3}. Let \overline{C E} and \overline{D F} intersect at G. If the area of \triangle C F G can be expressed as simplified fraction \frac{p}{q}, find p+q.