
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 $f(x) = ax^3$ ($a \neq 0$), consider the following statements:
1. $x = 0$ is an extreme point of $f(x)$.
2. When $a < 0$, $f(x)$ is a decreasing function on $(-\infty, +\infty)$.
3. The graph of $f(x)$ and the tangent line at $(1, f(1))$ must intersect at another point.

Identify the correct statement(s).

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