
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: $-(2-\sqrt{3})-{(\pi-3.14)}^{0}+(\frac{1}{2}-\cos30°) \times {(\frac{1}{2})}^{-2}$;<br/>$(2)$ Simplify first, then evaluate: $\frac{a-2}{{a}^{2}-4}-\frac{a+2}{{a}^{2}-4a+4}÷\frac{a+2}{a-2}$, where $a=\sqrt{3}$.

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