
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
$(1)$ Calculate: $tan60°×{({-2})^{-1}}-({\sqrt{\frac{3}{4}}-\sqrt[3]{8}})+|{-\frac{1}{2}\sqrt{12}}|$;<br/>$(2)$ Simplify and find the value: $({\frac{{x+2}}{{{x^2}-2x}}-\frac{{x-1}}{{{x^2}-4x+4}}})÷\frac{{x-4}}{x}$, where $x=\sqrt{2}+2$.

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