
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 satisfy
\begin{align*}
x + yz &= 9, \\
y + xz &= 12, \\
z + xy &= 12.
\end{align*}
Find the sum of all distinct $x$ values from the solutions $(x_1, y_1, z_1), (x_2, y_2, z_2), \dots, (x_n, y_n, z_n)$.

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