
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 $a$ is a real number, and $f(x)=(x^{2}-4)(x-a)$,

$(1)$ Find the derivative $f'(x)$;

$(2)$ If $x=-1$ is an extremum point of the function $f(x)$, find the maximum and minimum values of $f(x)$ on the interval $[-2,2]$;

$(3)$ If $f(x)$ is increasing on both $(-\infty,-2]$ and $[2,+\infty)$, find the range of values for $a$.

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