
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
Find all positive real numbers \(a\) and \(b\) such that for any \(n > 2\) and any non-negative real numbers \(x_1, x_2, \ldots, x_n\), the following inequality holds:
$$
x_1 x_2 + x_2 x_3 + \cdots + x_{n-1} x_n + x_n x_1 \geqslant x_1^a x_2^b x_3^a + x_2^a x_3^b x_4^a + \cdots + x_n^a x_1^b x_2^a.
$$

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