
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

Given the system of equations:

\[
\begin{cases}
  x_{1} x_{2} \cdot \ldots \cdot x_{1962} = 1 \\
  x_{1} - x_{2} x_{3} \cdot \cdots \cdot x_{1962} = 1 \\
  x_{1} x_{2} - x_{3} x_{4} \cdot \cdots \cdot x_{1962} = 1 \\
  \cdots \\
  x_{1} x_{2} \cdot \ldots \cdot x_{1961} - x_{1962} = 1
\end{cases}
\]

What values can \( x_{25} \) take?

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