HMMT 2019 G4

Convex hexagon $A B C D E F$ is drawn in the plane such that $A C D F$ and $A B D E$ are parallelograms with area 168. $A C$ and $B D$ intersect at $G$. Given that the area of $A G B$ is 10 more than the area of $C G B$, find the smallest possible area of hexagon $A B C D E F$.