
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 \( b \) forming an angle \( \theta \), and the length of their common perpendicular \( A' A \) is \( d \). Points \( E \) and \( F \) are taken on lines \( a \) and \( b \) respectively, with \( A' E = m \) and \( A F = n \). Find \( E F \). ( \( A' \) is on line \( a \), \( A \) is on line \( b \))

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