Triangle $ABC$ has $AB=25$, $AC=29$, and $BC=36$. Additionally, $\Omega$ and $\omega$ are the circumcircle and incircle of $\triangle ABC$. Point $D$ is situated on $\Omega$ such that $AD$ is a diameter of $\Omega$, and line $AD$ intersects $\omega$ in two distinct points $X$ and $Y$. Compute $XY^2$.

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