
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 \( x, y \in \mathbf{R} \) and satisfying the system of equations:

\[
\begin{cases}
(x+1)^{\frac{3}{5}} + 2023(x+1) = -2023, \\
(y+1)^{\frac{3}{5}} + 2023(y+1) = 2023
\end{cases}
\]

find the value of \( x + y \).

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