
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
Consider a function $y = f(x)$ defined over $\mathbb{R}$ with derivative $f'(x)$. If there exists an $x_0 \in [a, b]$ such that $f(b) - f(a) = f'(x_0)(b-a)$ holds, then $x_0$ is called a "mean value point" of the function $f(x)$ over the interval $[a, b]$. Determine the number of "mean value points" for the function $f(x) = x^3 - 3x$ over the interval $[-2, 2]$.

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