
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 \[f(x) =
\begin{cases}
x^3 + 3 &\text{if } x < n, \\
3x + 6 &\text{if } x \ge n.
\end{cases}
\]If the graph $y=f(x)$ is continuous at $x=n$, find the sum of all possible values of $n$.

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