
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 \[g(n) = \left\{
\begin{array}{cl}
n^2-5 & \text{ if }n<0, \\
3n-25 & \text{ if }n \geq 0.
\end{array}
\right.\] Determine the positive difference between the two values of $b$ that satisfy the equation $g(-3)+g(3)+g(b)=0$.

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