
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 $f(x) = x|x-2a| + a^2 - 4a$ ($a \in \mathbb{R}$).
- (I) When $a = -1$, find the maximum and minimum values of $f(x)$ on the interval $[-3, 0]$.
- (II) If the equation $f(x) = 0$ has three distinct real roots $x_1$, $x_2$, $x_3$, find the range of $\frac{1}{x_1} + \frac{1}{x_2} + \frac{1}{x_3}$.

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