
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 as:
\[
g(x) =
\begin{cases}
(x+1)^2-3 &\quad \text{if } x \ge -2, \\
x + 2 &\quad \text{otherwise},
\end{cases}
\]
Find how many values of $x$ exist such that $g(g(x)) = 4$.

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