
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/>$(1)\sqrt{2}(2-\sqrt{2})$;<br/>$(2)\sqrt{6}÷\sqrt{3}×\sqrt{24}$;<br/>$(3)\sqrt{54}+\sqrt{24}-\sqrt{18}+2\sqrt{\frac{1}{2}}$;<br/>$(4)(\sqrt{2}-1)^{2}-(\sqrt{5}+2)\times (\sqrt{5}-2)$.

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