
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$ -gon and  $ P_2$  be a regular  $ s$ -gon  $ (r\geq s\geq 3)$  such that each interior angle of  $ P_1$  is  $ \frac {59}{58}$  as large as each interior angle of  $ P_2$ . What's the largest possible value of  $ s$ ?

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