
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 two equiangular polygons \( P_1 \) and \( P_2 \) with \( n \) and \( m \) sides respectively such that \( m = n + k \) where \( k \) is a positive integer, and each angle of \( P_2 \) is 1.5 times each angle of \( P_1 \), find all possible values for \( n \) if \( k = 1 \).

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