
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
On the diagonal \( AC \) of the lower face of a unit cube \( ABCD A_{1} B_{1} C_{1} D_{1} \), a segment \( AE \) of length \( l \) is marked. On the diagonal \( B_{1} D_{1} \) of its upper face, a segment \( B_{1} F \) of length \( ml \) is marked. For which \( l \) (with fixed \( m > 0 \)) will the length of the segment \( EF \) be minimal?

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