
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
Given a tetrahedron \( A B C D \) with side lengths \( A B = 41 \), \( A C = 7 \), \( A D = 18 \), \( B C = 36 \), \( B D = 27 \), and \( C D = 13 \), let \( d \) be the distance between the midpoints of edges \( A B \) and \( C D \). Find the value of \( d^{2} \).

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