
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:<br/>$(1)(1+\sqrt{3})(2-\sqrt{3})$;<br/>$(2)\frac{\sqrt{36}×\sqrt{12}}{\sqrt{3}}$;<br/>$(3)\sqrt{18}-\sqrt{8}+\sqrt{\frac{1}{8}}$;<br/>$(4)(3\sqrt{18}+\frac{1}{5}\sqrt{50}-4\sqrt{\frac{1}{2}})÷\sqrt{32}$.

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