
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 $f(x) = x^3 + ax^2 + bx$ (where constants $a, b \in \mathbb{R}$), and $g(x) = f(x) - f'(x)$ is an odd function,
(1) Find the expression for $f(x)$;
(2) Find the maximum and minimum values of $g(x)$ on the interval $[1, 3]$.

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