
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
$(1)\sqrt{27}-\frac{1}{3}\sqrt{18}-\sqrt{12}$；<br/>$(2)\sqrt{48}+\sqrt{30}-\sqrt{\frac{1}{2}}×\sqrt{12}+\sqrt{24}$；<br/>$(3)(2-\sqrt{5})(2+\sqrt{5})-(2-\sqrt{2})^{2}$；<br/>$(4)\sqrt[3]{27}-\frac{\sqrt{2}×\sqrt{6}}{\sqrt{3}}$.

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