
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
Let \[g(x) = \left\{ \begin{aligned}
3x + 12 & \quad \text{if } x < -1 \\
x^2 - 1 & \quad \text{if } -1 \le x < 1 \\
2x + 1 & \quad \text{if } x \ge 1 
\end{aligned} \right.\]
Find all solutions to the equation $g(x) = 12.$

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