
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
Let \[g(x) = \left\{
\begin{array}{cl}
x^2 - 4 &\text{ if }x > 3, \\
5x + 2 &\text{ if } -3 \le x \le 3, \\
0 &\text{ if } x < -3.
\end{array}
\right.\]Find $g(-4)+g(0)+g(4)$.

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