
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: (1) $(\sqrt{27}-\sqrt{12}) \times \sqrt{\frac{1}{3}}$; (2) $(\sqrt{2023}+1)(\sqrt{2023}-1)+\sqrt{8} \div \sqrt{2}$.

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