
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
If there exist real numbers \(a, x, y\) such that the equation \(x \sqrt{a(x-a)} + y \sqrt{a(y-a)} = \sqrt{\log (x-a) - \log (a-y)}\) holds, determine the value of \(\frac{3x^2 + xy - y^2}{x^2 - xy + y^2}\).

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