
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
If \[g(x) =
\begin{cases}
x^2 + 1 &\quad \text{if } x \ge 0, \\
x - 2 &\quad \text{otherwise},
\end{cases}
\] then for how many values of $x$ is $g(g(x)) = 10$?

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