
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
Calculate (1) $-202 \cdot 3^{0}+{(-\frac{1}{2})}^{-2} \times |-1+3|+\sqrt{12}$.  
(2) Below is Xiaoying's process of simplifying fractions. Please read carefully and complete the corresponding tasks:  
$(\frac{x-1}{x+1}-\frac{{x}^{2}-1}{{x}^{2}-2x+1})÷\frac{x}{x-1}$:  
$=[\frac{x-1}{x+1}-\frac{(x-1)(x+1)}{{(x-1)}^{2}}]÷\frac{x}{x-1}\ldots \ldots \ldots \ldots $ Step one;  
$=(\frac{x-1}{x+1}-\frac{x+1}{x-1})÷\frac{x}{x-1}\ldots \ldots \ldots \ldots $ Step two;  
$=\frac{{(x-1)}^{2}-{(x+1)}^{2}}{(x+1)(x-1)}÷\frac{x}{x-1}\ldots \ldots \ldots \ldots $ Step three;  
$=\frac{{x}^{2}-2x+1-{x}^{2}+2x+1}{(x+1)(x-1)}⋅\frac{x-1}{x}\ldots \ldots \ldots \ldots $ Step four;  
$=\frac{2}{x(x+1)}\ldots \ldots \ldots \ldots $ Step five;  
$=\frac{2}{{x}^{2}+x}\ldots \ldots \ldots \ldots $ Step six;  
Task one: Fill in the blanks:  
1. In the first step of the simplification process, transforming the term $\frac{{x}^{2}-1}{{x}^{2}-2x+1}$ into $\frac{(x-1)(x+1)}{{(x-1)}^{2}}$ belongs to ______;  
$A$. Polynomial multiplication  
$B$. Factorization  
2. In the simplification process, step ______ is to find a common denominator for the fractions, based on ______;  
3. Error starts to appear in step ______, the specific reason for the error is ______.  
Task two: Please write down the correct result after simplifying the fraction.

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