
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 the rectangular parallelepiped $A B C D A_{1} B_{1} C_{1} D_{1}$, the lengths of the edges are given as $A B=54, A D=90, A A_{1}=60$. A point $E$ is marked at the midpoint of edge $A_{1} B_{1}$, and a point $F$ is marked at the midpoint of edge $B_{1} C_{1}$. Find the distance between lines $A E$ and $B F$.

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