
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 \( x \) and \( y \) are distinct nonzero real numbers such that \( x + \frac{3}{x} = y + \frac{3}{y} \), what is \( xy \)?
**A)** \( \frac{1}{4} \)  
**B)** \( \frac{1}{2} \)  
**C)** \( 1 \)  
**D)** \( 3 \)  
**E)** \( 4 \)

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