
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 convex polygons P_1 and P_2, with n_1 and n_2 sides respectively, where n_1 ≤ n_2, and P_1 has k sides (k ≤ n_1) intersecting with the sides of P_2, calculate the maximum number of intersections between P_1 and P_2.

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