
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 convex polygons P<sub>1</sub> and P<sub>2</sub> with different numbers of sides, each angle of P<sub>1</sub> measures x degrees, and each angle of P<sub>2</sub> measures kx degrees, where k is an integer greater than 1, determine the number of possible pairs (x, k).

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