
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
Let \( V \) be a set of 2019 points in space such that no four points are coplanar. Some points are connected by line segments. Let \( E \) be the set of these line segments. Find the smallest positive integer \( n \) such that if \( E \) has at least \( n \) elements, then \( E \) must contain 908 two-element subsets, where each two-element subset consists of line segments sharing a common endpoint, and the intersection of any two such subsets is empty.

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