
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
Any positive integer $n$ can be decomposed as follows: $n=s\times t$ ($s$, $t$ are positive integers, and $s\leqslant t$). If $p\times q$ has the smallest absolute difference between its two factors in all such decompositions of $n$, we call $p\times q$ the best decomposition of $n$, and define: $F(n)=\frac{p}{q}$. For example, $18$ can be decomposed into $1\times 18$, $2\times 9$, $3\times 6$, then we have $F(18)=\frac{3}{6}=\frac{1}{2}$. Given the following statements about $F(n)$: (1) $F(2)=\frac{1}{2}$; (2) $F(24)=\frac{3}{8}$; (3) $F(27)=3$; (4) If $n$ is a square of an integer, then $F(n)=1$. The correct statements are ____.

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