
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 \(ABCDA_1B_1C_1D_1\), the lengths of the edges are given as \(AB=60\), \(AD=30\), and \(AA_1=15\). 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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