Let $ABC$ be a triangle with $AB = 3$, $BC = 4$, and $CA = 5$. The line through $A$ perpendicular to $AC$ intersects line $BC$ at $D$, and the line through $C$ perpendicular to $AC$ intersects line $AB$ at $E$. Compute the area of triangle $BDE$.

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