
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 $x, y, x^2 - \frac{1}{y}$, and $y^2 - \frac{1}{x}$ are non-zero, evaluate the expression $\frac{x^2 - \frac{1}{y}}{y^2 - \frac{1}{x}}$.

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