
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
Find all  $n$ -tuples of reals  $x_1,x_2,\ldots,x_n$  satisfying the system:  $$ \begin{cases}x_1x_2\cdots x_n=1x_1-x_2x_3\cdots x_n=1x_1x_2-x_3x_4\cdots x_n=1\vdotsx_1x_2\cdots x_{n-1}-x_n=1\end{cases} $$  

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