
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 the function $g(x)$ is given. How many values of $x$ satisfy $g(g(x)) = 4$? The function $g(x)$ is defined as follows: $g(x) = 2$ for $x \leq -2$, $g(x) = x^2$ for $-2 < x \leq 2$, and $g(x) = 5$ for $x > 2$.

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