
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:  
$(1) \sqrt[3]{27}-\frac{\sqrt{2} \times \sqrt{6}}{\sqrt{3}}$;  
$(2) 2\sqrt{32}-\sqrt{50}$;  
$(3) \sqrt{12}-\sqrt{8}+\sqrt{\frac{4}{3}}+2\sqrt{\frac{1}{2}}$;  
$(4) \sqrt{48}+\sqrt{3}-\sqrt{\frac{1}{2}} \times \sqrt{12}+\sqrt{24}$.

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