
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:

$$
\begin{array}{ll}
x^{3} y^{2} z=2 & z^{3} u^{2} x=32 \\
y^{3} z^{2} u=8 & u^{3} x^{2} y=8
\end{array}
$$

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