In triangle $ABC$, let $O$ be the circumcenter and $G$ be the centroid. The line perpendicular to $OG$ at $O$ intersects $BC$ at $M$ such that $M$, $G$, and $A$ are collinear, and $OM = 3$. Compute the area of $\triangle ABC$, given that $OG = 1$.

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