
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 the following system of equations:

$$
\left\{\begin{array}{l}
x y + 2 x z + 3 y z = -6 \\
x^{2} y^{2} + 4 x^{2} z^{2} - 9 y^{2} z^{2} = 36 \\
x^{3} y^{3} + 8 x^{3} z^{3} + 27 y^{3} z^{3} = -216
\end{array}\right.
$$

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