
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
The graph of \( y = f(x) \) is shown below, with \( 1 \) unit between grid lines. Assume \( f(x) \) is defined only on the domain shown.

What is the sum of all integers \( c \) for which the equation \( f(x) = c \) has exactly \( 4 \) solutions?

[asy]
size(150);
rr_cartesian_axes(-6,6,-7,7);
real f(real x) {return (x-5)*(x-3)*(x-1)*(x+1)*(x+3)*(x+5)/315-3.4;}
draw(graph(f,-5.5,5.5,operator ..), red);
[/asy]

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