
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 $f(x) = ax^3 + bx^2 + x$ is an odd function, and $f(1) - f(-1) = 4$.
(1) Find the values of the real numbers $a$ and $b$;
(2) If for any $x \in [0, 2]$, $f(x) < c^2 - 9c$ always holds, find the range of the real number $c$.

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