
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 that satisfy
\[ 
\begin{cases} 
(x-1)^{3}+1997(x-1)=-1, \\
(y-1)^{3}+1997(y-1)=1 
\end{cases}.
\]

Then, \( x + y = \) ?

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