
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
Given \( x, y, z \) are nonnegative real numbers. For any \( x, y, z \), it holds that
\[
\begin{array}{l}
x^{3}+y^{3}+z^{3}-3xyz \\
\geqslant k |(x-y)(y-z)(z-x)|,
\end{array}
\]
find the maximum value of \( k \).

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