
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
Determine the pair of integers \( (x, k) \) for which one can form two distinct regular polygons \( P_1 \) and \( P_2 \) such that each angle of \( P_1 \) is \( x \) degrees and each angle of \( P_2 \) is \( kx \) degrees, with \( k \) being an integer and \( 1 < k < 5 \).
A) (60, 2)
B) (45, 4)
C) (75, 2)
D) (80, 3)

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