
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/>$(1)2\sqrt{7}-6\sqrt{7}$;<br/>$(2)\sqrt{\frac{2}{3}}÷\sqrt{\frac{8}{27}}$;<br/>$(3)\sqrt{18}+\sqrt{98}-\sqrt{27}$;<br/>$(4)(\sqrt{0.5}+\sqrt{6})-(\sqrt{\frac{1}{8}}-\sqrt{24})$.

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