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

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