A Focal Triangle Area from a Bisector

The hyperbola $C:x^2-\dfrac{y^2}{24}=1$ has left and right foci $F_1$, $F_2$. Let $P$ be a point of $C$ in the first quadrant, and let $l$ be the bisector of $\angle F_1PF_2$. The line through the origin $O$ parallel to $PF_2$ meets $PF_1$ and $l$ at points $M$ and $N$ respectively. If $|MN|=\dfrac 23|PF_2|$, find the area of $\triangle PF_1F_2$.