
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 $P_3$ where each angle of $P_1$ is $x$ degrees and each angle of $P_3$ is $kx - 10^\circ$ degrees, determine the number of possibilities for the pair $(x, k)$ assuming $k$ is an integer and $k > 1$. Choose the best answer among the following options:
A) Infinite possibilities
B) Exactly 2 possibilities
C) Exactly 3 possibilities
D) Exactly 1 possibility
E) No possibilities
A) Infinite possibilities
B) Exactly 2 possibilities
C) Exactly 3 possibilities
D) Exactly 1 possibility
E) No possibilities

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