
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
The area of a regular $n$-sided polygon inscribed in a unit circle is denoted as $f(n)$, where $n \geqslant 3$. Then, $f(3)=$ ______; The following statements describe $f(n)$:
1. $f(n)= \frac{n}{2}\sin \frac{2\pi}{n}$
2. The maximum value of $f(n)$ is $\pi$
3. $f(n) < f(n+1)$
4. $f(n) < f(2n) \leqslant 2f(n)$

Among these, the correct statement(s) is/are ______. (Note: Please list all correct statement numbers.)

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