
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
In space, there are 4 pairwise skew lines \( l_{1}, l_{2}, l_{3}, l_{4} \), such that no three of them are parallel to the same plane. Draw a plane \( P \) such that the points \( A_{1}, A_{2}, A_{3}, A_{4} \) at the intersections of these lines with \( P \) form a parallelogram. How many lines do the centers of such parallelograms trace out?

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