
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  
$(1)(2\sqrt{3}-1)^{2}+(\sqrt{3}+2)(\sqrt{3}-2)$  
$(2)(\sqrt{6}-2\sqrt{15})\times \sqrt{3}-6\sqrt{\frac{1}{2}}$.

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