
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 the equation \(\sqrt{a(x-a)}+\sqrt{a(y-a)}=\sqrt{x-a}-\sqrt{a-y}\) holds in the range of real numbers, where \(a, x, y\) are distinct real numbers, simplify the expression \(\frac{3x^2 + xy - y^2}{x^2 - xy + y^2}\).

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