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

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