In convex quadrilateral $ABCD$, $AB=BC=13$, $CD=DA=24$, and $\angle D=60^\circ$. Points $X$ and $Y$ are the midpoints of $\overline{BC}$ and

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In convex quadrilateral $ABCD$, $AB=BC=13$, $CD=DA=24$, and $\angle D=60^\circ$. Points $X$ and $Y$ are the midpoints of $\overline{BC}$ and $\angle D=60^\circ$. Points $X$ and $Y$ are the midpoints of $\overline{BC}$ and $/overline{DA}$ repectively. Compute $XY^2$(the square length $XY$).