
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 the following:<br/>$(1)(\frac{1}{3})^{-1}+\sqrt{12}-|\sqrt{3}-2|-(π-2023)^0$;<br/>$(2)\sqrt{\frac{2}{3}}-2\sqrt{24}+12\sqrt{\frac{1}{6}}$;<br/>$(3)(2\sqrt{5}-1)^2-(\sqrt{2}-1)(1+\sqrt{2})$.

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