
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 \( \frac{29}{28} \) 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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