
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: $|2-\sqrt{3}|+(\sqrt{2}+1)^0+3\tan30°+(-1)^{2023}-(\frac{1}{2})^{-1}$.  
$(2)$ Simplify first and then find the value: $(\frac{x-1}{x}-\frac{x-2}{x+1})÷\frac{2x^2-x}{x^2+2x+1}$, where $x$ satisfies $x^{2}-2x-2=0$.

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