
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 equations

\[ 1 - x_{1} x_{2} x_{3} = 0 \]

\[ 1 + x_{2} x_{3} x_{4} = 0 \]

\[ 1 - x_{3} x_{4} x_{5} = 0 \]

\[ 1 + x_{4} x_{5} x_{6} = 0 \]

...

\[ 1 - x_{47} x_{48} x_{49} = 0 \]

\[ 1 + x_{48} x_{49} x_{50} = 0 \]

\[ 1 - x_{49} x_{50} x_{1} = 0 \]

\[ 1 + x_{50} x_{1} x_{2} = 0 \]

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