
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
Define the function $f(n)$ as follows:
\[ f(n) = \left\{
\begin{array}{cl}
n^2 + 2n & \text{ if } n < -1, \\
e^n - 10 & \text{ if } n \geq -1.
\end{array}
\right. \]
Find the positive difference between the two values of $a$ that satisfy $f(-3) + f(0) + f(a) = 0$.

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