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

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