
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 tetrahedron $ABCD$, all the opposite edges are equal. Points $E$ and $F$ are the midpoints of $AB$ and $CD$ respectively, and $EF \perp AB$, $EF \perp CD$, with $EF = 6$, $AC = 10$, and $BC = 6\sqrt{2}$. What is the distance between the skew lines $AD$ and $BC$?

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