
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: $(-\frac{1}{2})^{-1} + \sqrt{2} \times \sqrt{6} - (\pi - 3)^{0} + |\sqrt{3} - 2|$;  
(2) Simplify: $\frac{x^{2}-1}{x+1} \div \frac{x^{2}-2x+1}{x^{2}-x}$.

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