
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 the graph of the quadratic function \(y = g(x)\) defined by \(g(x) = \frac{x^2}{2} - x - 2\). The distance between grid lines is 1 unit.

Find the sum of all distinct numbers \(x\) such that \(g(g(g(x))) = -2\).

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