
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
Simplify the following expression:
\[ \frac{\left(a b (x^{2}+y^{2}) + x y (a^{2}+b^{2}) \right) \cdot \left((a x+b y)^{2} - 4 a b x y \right)}{a b (x^{2}-y^{2}) + x y (a^{2}-b^{2})} \]

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