
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:<br/>$(1)\sqrt{12}×\sqrt{3}-5$;<br/>$(2)\sqrt{2}+\sqrt{18}-6\sqrt{\frac{1}{2}}$;<br/>$(3)(\sqrt{8}×\sqrt{3}-\sqrt{12})÷\sqrt{6}$;<br/>$(4)\frac{5}{\sqrt{3}}+(\sqrt{5}+2)^{0}-\sqrt{8}×\sqrt{2}$;<br/>$(5)\sqrt[3]{-27}+|\sqrt{5}-4|+|1-\sqrt{5}|$;<br/>$(6)(\sqrt{3}-\sqrt{2})^{2}-(\sqrt{6}+1)(\sqrt{6}-1)$.

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