In the parallelogram $ABCD$, we are given that $AC = 10$ and $BD = 28$. The points $K$ and $L$ are such that they move in the plane of $ABCD$ satisfying $AK = BD$ and $BL = AC$. Let $M$ and $N$ be the midpoints of $CK$ and $DL$, respectively. Determine the maximum value of the expression $\cot^2 \left(\frac{\angle BMD}{2}\right) + \tan^2 \left(\frac{\angle ANC}{2}\right)$.

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