
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 a \(60^\circ\) angle and have a common perpendicular segment \(EF\) with \(|EF| = 2\). The length of the segment \(AB\) is 4, with endpoints \(A\) and \(B\) moving on \(a\) and \(b\) respectively. Find the equation of the locus of the midpoint \(P\) of the segment \(AB\).

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