
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 that $x, y\in \mathbb{R}$ and they satisfy the system of equations $\begin{cases}(x-2)^{3}+2x+\sin (x-2)=2\\\\(y-2)^{3}+2y+\sin (y-2)=6\end{cases}$, calculate the value of $x+y$.

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