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

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