In the convex quadrilateral $ABCD$, we have the following side lengths: $AB = 15$, $BC = 16$, $CD = 12$, $DA = 25$, and the diagonal $BD = 20$. Let $M$ be the circumcenter and $\gamma$ the circumcircle of $\triangle ABD$. Line $CB$ intersects $\gamma$ again at point $F$. Line $AF$ intersects $MC$ at point $G$, and line $GD$ intersects $\gamma$ again at point $E$. Determine the area of the pentagon $ABCDE$.

Let's think step by step and output the final answer within \boxed{}.
user