
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  $n \ge 3$  solve in real numbers the system of equations:  $$ \begin{cases}  x_1^3 = x_2 + x_3 + 1 ...x_{n-1}^3 = x_n+ x_1 + 1x_{n}^3 = x_1+ x_2 + 1 \end{cases} $$  

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