
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 \[ f(n) = \left\{
\begin{array}{cl}
n^2 - 6 & \text{if } n < 1, \\
3n - 15 & \text{if } n \geq 1.
\end{array}
\right. \]
What is the positive difference between the two values of $b$ that satisfy the equation $f(-1) + f(1) + f(b) = 0$?

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