
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 a set $V$ of 2019 points in space where no four points lie on the same plane, and a set $E$ of line segments connecting some of these points, find the smallest positive integer $n$ such that if $E$ contains at least $n$ elements, it must include 908 pairs of line segments, each having a common endpoint, and no two pairs have overlapping segments.

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