
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 $y=g(x)$ described by the polynomial $g(x) = \frac{(x - 6)(x - 4)(x - 2)(x)(x + 2)(x + 4)}{360} - 5$. Determine the sum of all integers $c$ for which the equation $g(x) = c$ has exactly 8 solutions. The function is defined only on the domain shown in the graph.

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