
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: $(1-\sqrt{3})^{0}-|-\sqrt{2}|+\sqrt[3]{-27}-{(-\frac{1}{2})}^{-1}$;  
$(2)$ Simplify: $\left(\frac{x^{2}-1}{x-2}-x-1\right) \div \frac{x+1}{x^{2}-4x+4}$, choose an appropriate number to substitute and find the value.

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