Let $ABC$ be a right triangle with a right angle at $C$. Two lines, one parallel to $AC$ and the other parallel to $BC$, intersect on the hypotenuse $AB$. These lines split the triangle into two triangles and a rectangle. The two triangles have areas $512$ and $32$. What is the area of the rectangle?

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