
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 entire graph of function $g(x)$ defined only for $x$ between $-5$ and $5$ inclusive. The graph includes three segments: the first segment is a downward-opening parabola from $x = -5$ to $x = -1$, the second segment is a straight line from $x = -1$ to $x = 3$, and the third segment is an upward-opening parabola from $x = 3$ to $x = 5$. How many values of $x$ satisfy $g(g(x)) = 3$?

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