
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
Let \(P_1\) be a regular \(r\)-sided polygon and \(P_2\) be a regular \(s\)-sided polygon with \(r \geq s \geq 3\), such that each interior angle of \(P_1\) is \(\frac{61}{60}\) as large as each interior angle of \(P_2\). What is the largest possible value of \(s\)?

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