
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 \( A B C D A_{1} B_{1} C_{1} D_{1} \), the edge lengths are given as \( A B = 48 \), \( A D = 24 \), and \( A A_{1} = 12 \). 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 \( A E \) and \( B F \).

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