
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: $\sqrt{12}-4|\sin 60^{\circ}|+{(\frac{1}{3})}^{-1}-\left(2023-\pi \right)^{0}$;<br/>$(2)$ Simplify first, then evaluate: $(1+\frac{3}{x-5})÷\frac{{x}^{2}-4x+4}{2x-10}$, where $x=\sqrt{2}+2$.

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