
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
For any positive numbers \( a_{1}, a_{2}, \cdots, a_{n} \), let \( a_{n+1} = a_{1} \). Is the inequality

\[ \sum_{i=1}^{n}\left(\frac{a_{i}}{a_{i+1}}\right)^{n} \geq \sum_{i=1}^{n} \frac{a_{i+1}}{a_{i}} \]

true?

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