
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 \[f(x) =
\begin{cases}
x^2-2 &\quad \text{if } x \ge 2, \\
x + 4 &\quad \text{otherwise},
\end{cases}
\]then for how many values of $x$ is $f(f(x)) = 7$?

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