
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
Given the real numbers \( (x, y) \) satisfy the system of equations \[
\begin{cases}
x^{3} - 6x^{2} + 12x = 13, \\
y^{3} + 3y - 3y^{2} = -4,
\end{cases}
\]
find \( x + y \).

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