
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 $ABCDEFGH$, the edge lengths are given as $AB = 30$, $AD = 32$, and $AA_1 = 20$. Point $E$ is marked at the midpoint of edge $A_1B_1$, and point $F$ is marked at the midpoint of edge $B_1C_1$. Find the distance between the lines $AE$ and $BF$.

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