
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/>$(1)3\sqrt{3}+\sqrt{8}-\sqrt{2}+\sqrt{27}$;<br/>$(2)\frac{1}{2}(\sqrt{3}+\sqrt{5})-\frac{3}{4}(\sqrt{5}-\sqrt{12})$;<br/>$(3)(2\sqrt{5}+\sqrt{6})(2\sqrt{5}-\sqrt{6})-{(\sqrt{5}-\sqrt{6})}^{2}$.

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