
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 \[f(n) = \left\{
\begin{array}{cl}
n^2 + 4 & \text{ if } n < 3, \\
2n - 30 & \text{ if } n \geq 3.
\end{array}
\right.\]
What is the positive difference between the two values of \(x\) that satisfy the equation \(f(-3) + f(3) + f(x) = 0\)?

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