
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 portion of the graph of \( y = g(x) \) is shown where \( g(x) \) is a cubic function defined by \( g(x) = \frac{x^3}{8} - \frac{3x}{2} - 2 \). Determine the sum of all distinct \( x \) such that \( g(g(g(x))) = 2 \).

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