
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 \( n \) line segments in space, no three of which are parallel to the same plane, and for which the midpoint connection between any two segments is the common perpendicular of those segments, find the maximum possible value of \( n \).

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