
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 \( x, y, z \) be positive integers. The sets are defined as
\[
\begin{aligned}
A= & \{3(x-y)(y-z)(z-x), x y z, \\
& 2\left(y^{2} z^{2}+z^{2} x^{2}+x^{2} y^{2}\right)\}, \\
B= & \left\{(x-y)^{3}+(y-z)^{3}+(z-x)^{3}, x+y+z, x^{4}+y^{4}+z^{4}\right\}.
\end{aligned}
\]
If \( A=B \), then \( x^{3}+y^{3}+z^{3} \) equals ________.

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