
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 a piecewise cubic function $g(x)$ defined and graphed on the interval $-5 \leq x \leq 5$. Determine how many values of $x$ meet the condition $g(g(x)) = 3$.

[Picture here of a piecewise cubic function graphed from $x = -5$ to $x = 5$. Assume the intersections with the line $y = 3$ occur at distinct points $x_1, x_2, x_3$ within this range.]

[Note: Due to backend text constraints, the actual graph is hypothetical but should depict the function intersecting y=3 at three clear points.]

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