
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 one of the nodes of a hexagon with side length \( n \), divided into equilateral triangles (see the picture), there is a token. Two players take turns moving it to one of the adjacent nodes, with the rule that it is forbidden to move to a node that the token has already visited. The player who cannot make a move loses. Who wins with perfect play?

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