Suppose $x, y, z$, and $w$ are positive reals such that:
\[ x^2 + y^2 - \frac{xy}{2} = w^2 + z^2 + \frac{wz}{2} = 36 \]
\[ xz + yw = 30. \]
Find the largest possible value of $(xy + wz)^2$.

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