
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
If the function $f(x)$ takes an extreme value at $x = x$, then the point $(x, f(x))$ is called an extreme point of the function $f(x)$. It is known that the function $f(x) = ax^3 + bx^2 + cx + d$ ($a \neq 0$, $a, b, c, d \in \mathbb{R}$) has an extreme point exactly at the origin of the coordinate system, and the equation of the tangent line to $y = f(x)$ at $x = 1$ is $3x + y - 1 = 0$.
(1) Find the expression of the function $f(x)$;
(2) Find the range of the function $f(x)$ on $[-2, 2]$.

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