
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 following system of equations:

$$
\left\{\begin{array}{r}
x_{1} \cdot x_{2} \cdot \ldots \cdot x_{n}=1 \\
x_{1}-x_{2} \cdot x_{3} \cdot \ldots \cdot x_{n}=1 \\
x_{1} \cdot x_{2}-x_{3} \cdot x_{4} \cdot \ldots \cdot x_{n}=1 \\
\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \\
x_{1} \cdot x_{2} \cdot \ldots \cdot x_{n-1}-x_{n}=1
\end{array}\right.
$$

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