
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 graphs of two functions, $f(x)$ and $g(x)$, are given. The function $f(x) = |x| - 3$ and $g(x) = -x$. If $f(g(f(x)))$ is evaluated at $x= -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5$, what is the sum of the eleven values obtained?

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