
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 a rectangular parallelepiped \( ABCD A_1 B_1 C_1 D_1 \), the lengths of the edges are known: \( AB = 60 \), \( AD = 36 \), \( AA_1 = 40 \). Point \( E \) is marked at the midpoint of edge \( A_1 B_1 \), and point \( F \) is marked at the midpoint of edge \( B_1 C_1 \). Find the distance between the lines \( AE \) and \( BF \).

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