
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
Define function $g(x)$ as:
\[
g(x) =
\begin{cases}
x^2 - 1 &\quad \text{if } x \ge -2, \\
x + 5 &\quad \text{otherwise},
\end{cases}
\]
Determine the number of values of $x$ for which $g(g(x)) = 9$.

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