
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: $(2+\sqrt{3})^{0}+3\tan 30^{\circ}-|{\sqrt{3}-2}|+{(\frac{1}{2})^{-1}}$<br/>$(2)$ Simplify first, then find the value: $\frac{{{a^2}-9}}{{{a^2}-3a}}÷(\frac{{{a^2}+9}}{a}+6)$, where $a^{2}-4a+3=0$.

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