
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 \( x_{i} \) (for \( i = 0, 1, \cdots, n \)) be positive numbers, with \( n \geq 2 \) and \( n \in \mathbf{N} \). Then,
\[ \left( \frac{x_{0}}{x_{1}} \right)^{n} + \left( \frac{x_{1}}{x_{2}} \right)^{n} + \cdots + \left( \frac{x_{n-1}}{x_{n}} \right)^{n} + \left( \frac{x_{n}}{x_{0}} \right)^{n} \geq \frac{x_{1}}{x_{0}} + \frac{x_{2}}{x_{1}} + \cdots + \frac{x_{n}}{x_{n-1}} + \frac{x_{0}}{x_{n}}.
\]

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