
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
For a positive integer \( n \), if \( n = p \cdot q \) (where \( p \geqslant q \) and \( p, q \in \mathbf{N}^{*} \)), and \( p - q \) is minimized, we call \( p \cdot q \) the "best decomposition" of \( n \), and define \( f(n) = \frac{q}{p} \). For example, the decompositions of 12 are \( 12 \times 1, 6 \times 2, 4 \times 3 \), among which \( 4 \times 3 \) is the best decomposition of 12, so \( f(12) = \frac{3}{4} \). Regarding \( f(n) \), there are the following four statements:
1. \( f(4) = 0 \);
2. \( f(7) = \frac{1}{7} \);
3. \( f(24) = \frac{3}{8} \);
4. \( f(2012) = \frac{4}{503} \).
Which of the statements are correct?

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