
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 a continuous function $g(x)$ on $\mathbb{R}$ satisfying the following conditions: (i) $g'(x) > 0$ for $x > 0$ always holds; (ii) for any $x \in \mathbb{R}$, $g(x) = g(-x)$. Also, a function $f(x)$ satisfies: for any $x \in \mathbb{R}$, $f(\sqrt{3} + x) = -f(x)$. When $x \in [0, \sqrt{3}]$, $f(x) = x^3 - 3x$. If the inequality $g[f(x)] \leq g(a^2 - a + 2)$ always holds for $x \in [-3, 3]$, then the range of values for $a$ is _______.

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