
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 $f(x)=-x^{3}+ax^{2}+bx+c$, it is known that the function is decreasing on $(-\infty,0)$ and increasing on $(0,1)$. The function $f(x)$ has three real roots, and $1$ is one of them.

(I) Find the value of $b$;

(II) Find the range of $f(2)$;

(III) Let $g(x)=x-1$, and the solution set of $f(x) > g(x)$ is $(-\infty,1)$, find the range of real number $a$.

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