
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 polynomial function $g(x) = \frac{(x-6)(x-4)(x-2)(x+2)(x+4)(x+6)}{400} - 4$. The graph of $y=g(x)$ is defined over the domain $x \in [-7,7]$. Calculate the sum of all integer values of $d$ for which the equation $g(x)=d$ has exactly 6 solutions.

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