
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
\(\frac{a+b}{(\sqrt{a}-\sqrt{b})^{2}} \cdot \left( \frac{3ab - b\sqrt{ab} + a\sqrt{ab} - 3b^{2}}{\frac{1}{2} \sqrt{\frac{1}{4} \cdot \left( \frac{a}{b} + \frac{b}{a} \right)^{2} - 1}} + \frac{4ab\sqrt{a} + 9ab\sqrt{b} - 9b^{2}\sqrt{a}}{\frac{3}{2} \sqrt{b} - 2 \sqrt{a}} \right)\)
where \(a > b > 0\).

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