Parallelogram $ABCD$ is given such that $\angle ABC = 30^\circ$. Let $X$ be the foot of the perpendicular from $A$ onto $BC$, and $Y$ the foot of the perpendicular from $C$ onto $AB$. If $AX = 20$ and $CY = 22$, find the area of the parallelogram.

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