Slopes in Geometric Progression

An ellipse centered at the origin $O$, with foci on the $x$-axis and eccentricity $\dfrac{\sqrt 3}2$, passes through the point $\left(\sqrt 2,\dfrac{\sqrt 2}2\right)$. A line $l$ not passing through $O$ meets the ellipse at two points $P$ and $Q$ such that the slopes of $OP$, $PQ$, $OQ$ form (in this order) a geometric progression.

Find the range of the area of $\triangle OPQ$.