
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In parallelogram  $ABCD$ ,  $AC=10$  and  $BD=28$ . The points  $K$  and  $L$  in the plane of  $ABCD$  move in such a way that  $AK=BD$  and  $BL=AC$ . Let  $M$  and  $N$  be the midpoints of  $CK$  and  $DL$ , respectively. What is the maximum walue of  $\cot^2 (\tfrac{\angle BMD}{2})+\tan^2(\tfrac{\angle ANC}{2})$  ?

Present the answer in LaTex format: \boxed{Your answer}
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