
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. $\sqrt{12}-|\sqrt{3}-3|+(\sqrt{3})^2$
2. $2\sqrt{18} \times \frac{\sqrt{3}}{4} \div 5\sqrt{2}$
3. $\frac{\sqrt{6}-\sqrt{3}}{\sqrt{3}}+(2+\sqrt{2})(2-\sqrt{2})$
4. $\frac{2}{3}\sqrt{9x}+6\sqrt{\frac{x}{4}}-2\sqrt{\frac{1}{x}}$ when $x=\sqrt{\frac{1}{x}}$

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