
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
Let the ordered triples \((x,y,z)\) of complex numbers that satisfy
\begin{align*}
x + yz &= 9, \\
y + xz &= 12, \\
z + xy &= 12.
\end{align*}
be \((x_1,y_1,z_1), (x_2,y_2,z_2), \dots, (x_n,y_n,z_n)\). Find \(x_1 + x_2 + \dots + x_n\).

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