
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 the function $f(x)=ax^{3}$, $(a\neq 0)$, the following statements are made:
1. $x = 0$ is an extreme point of $f(x)$.
2. When $a < 0$, $f(x)$ is a decreasing function over $(-\infty,+\infty)$.
3. The graph of $f(x)$ must intersect with the tangent at $(1,f(1))$ at another point.
4. When $a > 0$, $f(x)$ is a decreasing function over $(-\infty,+\infty)$.

The correct sequence number(s) for the statement(s) is/are __________.

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