
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
Given two skew lines \( l \) and \( m \), there are three points \( A, B, \) and \( C \) on \( l \), such that \( AB = BC \). Perpendicular lines \( AD, BE, \) and \( CF \) are drawn from \( A, B, \) and \( C \) respectively to the line \( m \), with foot points being \( D, E, \) and \( F \) accordingly. Given that \( AD = \sqrt{15} \), \( BE = \frac{7}{2} \), and \( CF = \sqrt{10} \), find the distance between \( l \) and \( m \).

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