
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
Solve the system of equations:

$$
\begin{aligned}
& x_{1}+x_{2}+x_{3}=6 \\
& x_{2}+x_{3}+x_{4}=9 \\
& x_{3}+x_{4}+x_{5}=3 \\
& x_{4}+x_{5}+x_{6}=-3 \\
& x_{5}+x_{6}+x_{7}=-9 \\
& x_{6}+x_{7}+x_{8}=-6 \\
& x_{7}+x_{8}+x_{1}=-2 \\
& x_{8}+x_{1}+x_{2}=2
\end{aligned}
$$

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