
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
Suppose the graph of \(y=g(x)\) is defined by the function \(g(x) = \frac{(x-6)(x-4)(x-2)(x)(x+2)(x+4)(x+6)}{1005} - 2.5\), defined only on the interval shown in the graph. Determine the sum of all integers \(c\) for which the equation \(g(x)=c\) has exactly \(8\) solutions.

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