
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 polynomial function $y = g(x)$. Assume $g(x)$ has real coefficients and is defined on the domain as shown in a hypothetical graph. What is the sum of all integers $c$ for which the equation $g(x)=c$ has exactly 8 solutions? Assume that the function behavior and selected intersections are such that the two horizontal lines $y = -2$ and $y = -3$ intercept the graph 8 times each.

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