
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 \( a \) and \( b \) that form an angle \( \theta \), and let the distance of their common perpendicular \( A'A \) be \( d \). Points \( E \) and \( F \) are taken on lines \( a \) and \( b \) respectively. Suppose \( A'E = m \) and \( AF = n \). Find the distance \( EF \). \( (A' \) is on line \( a \), and \( A \) is on line \( b \)).

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