In $\triangle ABC$, $AB = 10$, $BC = 8$, and $CA = 6$. A line parallel to $BC$ intersects $AB$ at $D$ and $AC$ at $E$, creating $\triangle ADE$ similar to $\triangle ABC$. The area of $\triangle ADE$ is $\frac{9}{25}$ of the area of $\triangle ABC$. What is the length of $DE$? Let's think step by step and output the final answer within \boxed{}.
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