
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 real solutions of the system of equations  $$ \begin{cases}  x^2 + y^2 + u^2 + v^2 = 4  xu + yv + xv + yu = 0   xyu + yuv + uvx + vxy = - 2  xyuv = -1 \end{cases} $$  

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