
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 the complex solutions for the following system of equations:
\[
\begin{cases}
x(x-y)(x-z) = 3, \\
y(y-x)(y-z) = 3, \\
z(z-x)(z-y) = 3.
\end{cases}
\]

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