
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 the following equations:
\begin{align*}
x + yz &= 9, \\
y + xz &= 12, \\
z + xy &= 12.
\end{align*}
Find the sum $x_1 + x_2 + \dots + x_n$ of all distinct $x$ values among the solutions.

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