
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
A section of the graph \( y = g(x) \), where \( g(x) \) is a quadratic function, is depicted. The \( y \)-coordinate values for which \( g(g(g(x))) = -2 \) need to be determined. The quadratic function is given by \( g(x) = \frac{x^2}{3} + x - 2 \).

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