
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 $ABCDA_{1}B_{1}C_{1}D_{1}$, the lengths of the edges are given as $AB=18$, $AD=30$, and $AA_{1}=20$. Point $E$ is marked on the midpoint of edge $A_{1}B_{1}$, and point $F$ is marked on 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}
user