
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:
$$
\left\{\begin{array}{l}
x_{1} + x_{2} + x_{3} = 6, \\
x_{2} + x_{3} + x_{4} = 9, \\
x_{3} + x_{4} + x_{5} = 3, \\
x_{4} + x_{5} + x_{6} = -3, \\
x_{5} + x_{6} + x_{7} = -9, \\
x_{6} + x_{7} + x_{8} = -6, \\
x_{7} + x_{8} + x_{1} = -2, \\
x_{8} + x_{1} + x_{2} = 2.
\end{array}\right.
$$

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