
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 \( x \) and \( y \) be real numbers that satisfy the following system of equations:
\[ 
\begin{cases} \frac{x}{x^{2} y^{2}-1}-\frac{1}{x}=4 \\ \frac{x^{2} y}{x^{2} y^{2}-1}+y=2 \end{cases} 
\]

Find all possible values of the product \( xy \).

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