
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
\[
\begin{cases}
1 - x_1 x_2 = 0, \\
1 - x_2 x_3 = 0, \\
1 - x_3 x_4 = 0, \\
\vdots \\
1 - x_{n-1} x_n = 0, \\
1 - x_n x_1 = 0.
\end{cases}
\]

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