
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 the function $f(x) = x^3 - 3x^2$, consider the following statements:  
(1) $f(x)$ is an increasing function with no extremum;  
(2) $f(x)$ is a decreasing function with no extremum;  
(3) The increasing intervals of $f(x)$ are $(-\infty, 0)$ and $(2, +\infty)$;  
(4) $f(0) = 0$ is a local maximum, and $f(2) = -4$ is a local minimum.  
Among these statements, the correct ones are (Note: Fill in the numbers of all correct statements).

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