
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 \[g(n) = \left\{
\begin{array}{cl}
n^2 + 3n + 2 & \text{ if } n \leq 0, \\
3n - 15 & \text{ if } n > 0.
\end{array}
\right.\]
What is the positive difference between the two values of \( b \) that satisfy the equation \( g(-1) + g(1) + g(b) = 0 \)?

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