
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 in the real numbers  $x, y, z$  a system of the equations:
\[
\begin{cases}
x^2 - (y+z+yz)x + (y+z)yz = 0   
y^2 - (z + x + zx)y + (z+x)zx = 0 
  z^2 - (x+y+xy)z + (x+y)xy = 0. 
\end{cases}
\]

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