
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 fifteen equations with fifteen unknowns:

\[
\left\{\begin{aligned}
1-x_{1} x_{2} & =0 \\
1-x_{2} x_{3} & =0 \\
1-x_{3} x_{4} & =0 \\
\cdots & \cdots \\
1-x_{14} x_{15} & =0 \\
1-x_{15} x_{1} & =0
\end{aligned}\right.
\]

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