
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: $(-\frac{1}{3})^{-1}-\sqrt{12}-(2-\sqrt{3})^{0}$;  
$(2)$ Simplify first, then evaluate: $(1+\frac{1}{x})+\frac{x^2-1}{x}$, where the value of $x$ can be chosen from $-1$, $0$, $1$, or $2$.

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