
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 \(0<x, y<1, n \in \mathbf{N}^{\cdot}\), compare \(\frac{x^{n}}{1-x^{2}}+\frac{y^{n}}{1-y^{2}}\) and \(\frac{x^{n}+y^{n}}{1-x y}\).

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