
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 $g(x)$ defined on the interval $[-4, 4]$ as follows:
$$ g(x) = \begin{cases} 
x^3 + x^2 - 2x & \text{if } -4 \leq x < 0 \\
2x - 4 & \text{if } 0 \leq x \leq 4 
\end{cases} $$
How many values of $x$ satisfy $g(g(x)) = 3$?

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