
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
For each integer  $n \ge 2$ , find all integer solutions of the following system of equations:

\[x_1 = (x_2 + x_3 + x_4 + ... + x_n)^{2018}\]
\[x_2 = (x_1 + x_3 + x_4 + ... + x_n)^{2018}\]
\[\vdots\]
\[x_n = (x_1 + x_2 + x_3 + ... + x_{n - 1})^{2018}\]

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