
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, $f(x)=(x^{2}-4)(x-a)$.
(1) Find the derivative $f′(x)$;
(2) If $f′(-1)=0$, find the maximum and minimum values of $f(x)$ on $[-2,2]$;
(3) If $f(x)$ is increasing on $(-∞,-2)$ and $(2,+∞)$, find the range of $a$.

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