
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 $Q_1$ be a regular $m$-gon and $Q_2$ be a regular $n$-gon ($m\geq n\geq 3$) such that each interior angle of $Q_1$ is $\frac{8}{7}$ times as large as each interior angle of $Q_2$. What is the largest possible value of $n$?

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