
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 function \( f(x) = \frac{(x-4)(x-2)(x)(x+2)(x+4)}{120} - 2 \), which is shown graphically with a 1-unit grid space. The graph portrays \( f(x) \) defined on a domain where the grid lines are visible. Determine the sum of all integer values \( c \) for which the equation \( f(x) = c \) has exactly 4 solutions.

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