
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 \( x, y, z > 0 \), and
\[ 
\begin{array}{l}
x^{3}+\frac{1}{y+2016}=y^{3}+\frac{1}{z+2016} \\
=z^{3}+\frac{1}{x+2016} .
\end{array}
\]

Determine the set of values of 
\[
\frac{x^{3}+y^{3}+z^{3}}{xyz}
\]

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