
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 $f(x)=- \frac {1}{3}x^{3}+2ax^{2}-3a^{2}x$ $(a\in\mathbb{R}$ and $a\neq 0)$.  
$(1)$ When $a=-1$, find the equation of the tangent line to the curve $y=f(x)$ at $(-2,f(-2))$;  
$(2)$ When $a > 0$, find the intervals of monotonicity and the extremum of the function $y=f(x)$;  
$(3)$ When $x\in[2a,2a+2]$, the inequality $|f'(x)|\leqslant 3a$ always holds, find the range of values for $a$.

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