
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 a plane, given \( n > 1 \) points, two players take turns connecting a yet unconnected pair of points with a vector in one of two possible directions. If after a player’s move, the sum of all drawn vectors is zero, the second player wins. If a move is no longer possible and there was no zero sum, the first player wins. Who wins with optimal play?

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