
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/>$(1)\sqrt{2}-\sqrt{8}+\sqrt{32}$<br/>$(2)(\sqrt{3}-\sqrt{2})^{2}-(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})$;<br/>$(3)(\sqrt{6}-2\sqrt{15})×\sqrt{3}-\sqrt{36}÷\sqrt{2}$<br/>$(4)\frac{\sqrt{8}-\sqrt{6}}{\sqrt{2}}+3\times \sqrt{\frac{1}{3}}($calculate in two ways).

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