
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 that \(0 \leq x_{i} \leq 1\) for \(i=1,2,\cdots, 5\), find the maximum value of
$$
\left|x_{1}-x_{2}\right|^{3}+\left|x_{2}-x_{3}\right|^{3}+\left|x_{3}-x_{4}\right|^{3}+
\left|x_{4}-x_{5}\right|^{3}+\left|x_{5}-x_{1}\right|^{3}
$$.

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