
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  
$(1)\sqrt{{{({-2})}^2}}-\sqrt[3]{{\frac{1}{8}}}+|{-\sqrt{3}}|$;  
$(2)\sqrt{36}+\sqrt[3]{{-64}}+|{1-\sqrt{2}}|-{({-1})^{2023}}$;  
$(3)\sqrt{7}×({1-\sqrt{7}})+\sqrt{7}×({\sqrt{7}-\frac{2}{{\sqrt{7}}}})$.

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