
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 a regular polygon with a perimeter of 60 and a side length of $a$:
(1) When $n=3$, please directly write out the value of $a$;
(2) After increasing both the perimeter and the number of sides of the regular polygon by 7, assuming the result is still a regular polygon, its number of sides is $n+7$, and its perimeter is 67, with a side length of $b$. Some people calculated the corresponding values of $a$ and $b$ for $n=3$, $20$, $120$, and then claimed: "No matter what positive integer greater than 2 is chosen for $n$, $a$ and $b$ will definitely not be equal." Do you think this statement is correct? If not, please find the value of $n$ that does not conform to this statement.

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