
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
Given the graph of \(y = g(x)\), where \(g(x) = \frac{(x-4)(x-2)(x)(x+2)(x+4)}{120} - 2.2\), determine the sum of all integer values \(c\) for which the equation \(g(x) = c\) has exactly 6 solutions. Assume \(g(x)\) is defined only where shown on its domain.

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