
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/>$(1)(\sqrt{\frac{1}{3}})^{2}+\sqrt{0．{3}^{2}}-\sqrt{\frac{1}{9}}$;<br/>$(2)(\sqrt{6}-\sqrt{\frac{1}{2}})-(\sqrt{24}+2\sqrt{\frac{2}{3}})$;<br/>$(3)(\frac{\sqrt{32}}{3}-4\sqrt{\frac{1}{2}}+3\sqrt{27})÷2\sqrt{2}$;<br/>$(4)(\sqrt{3}+\sqrt{2}-1)(\sqrt{3}-\sqrt{2}+1)$.

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