
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 \( x \) and \( y \) be real numbers satisfying the following system of equations:
\[
\begin{cases}
x^{3} - 3x^{2} + 2000x = 1997, \\
y^{3} - 3y^{2} + 2000y = 1999
\end{cases}
\]
What is \( x + y \)?

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