
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 $a$ and $b$ are real numbers, and $1$ and $-1$ are two extreme points of the function $f(x)=x^{3}+ax^{2}+bx$.
(1) Find the values of $a$ and $b$;
(2) Let the derivative of the function $g(x)$ be $g′(x)=f(x)+2$, find the extreme points of $g(x)$;
(3) Let $h(x)=f(f(x))-c$, where $c∈[-2,2]$, find the number of zeros of the function $y=h(x)$.

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