
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
Calculate the following:  
(1) $(3\sqrt{2} - \sqrt{12})(\sqrt{18} + 2\sqrt{3})$  
(2) $(\sqrt{5} - \sqrt{6})^2 - (\sqrt{5} + \sqrt{6})^2$  
(3) $(2\sqrt{\frac{3}{2}} - \sqrt{\frac{1}{2}})(\frac{1}{2}\sqrt{8} + \sqrt{\frac{2}{3}})$

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