
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 $x$, $y$ be real numbers, and 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