
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
$(1)\left(2021-\pi \right)^{0}+|\sqrt{3}-1|-(\frac{1}{2})^{-1+}\sqrt{12}$；  
$(2)(\sqrt{2}+\sqrt{3})(\sqrt{3}-\sqrt{2})+\sqrt{6}\times \sqrt{\frac{2}{3}}$；  
$(3)\frac{\sqrt{20}+\sqrt{5}}{\sqrt{5}}-6\sqrt{\frac{1}{3}}$.

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