
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 that the function $f(x) = -x^3 + ax^2 + bx + c$ is decreasing on $(-\infty, 0)$ and increasing on $(0, 1)$, and that $f(x)$ has three zeros on $\mathbb{R}$ with $1$ being one of the zeros.

(1) The value of $b$ is \_\_\_\_\_\_ ;  
(2) The range of values for $f(2)$ is \_\_\_\_\_\_ .

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