
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
Two players in turns color the sides of an  $n$ -gon. The first player colors any side that has  $0$  or  $2$  common vertices with already colored sides. The second player colors any side that has exactly  $1$  common vertex with already colored sides. The player who cannot move, loses. For which  $n$  the second player has a winning strategy?

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