
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
Below is the process of Xiao Bin's simplification of fractions. Please read carefully and solve the problem.

$\frac{{x}^{2}-1}{{x}^{2}+2x+1}÷(\frac{1}{x+1}-1)$, where the value of $x$ is selected from the integer solutions of $-2 \lt x \lt 2$.

$\frac{{x}^{2}-1}{{x}^{2}+2x+1}÷(\frac{1}{x+1}-1)$

$=\frac{{x}^{2}-1}{{x}^{2}+2x+1}⋅(x+1-1)\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $Step 1

$=\frac{{x}^{2}-1}{{x}^{2}+2x+1}⋅x\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $Step 2

$=\frac{(x+1)(x-1)}{(x+1)^{2}}⋅x\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $Step 3

$=\frac{x(x-1)}{x+1}\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $Step 4

Question: (1) The error starts from step ____, and the reason for this error is ____.

(2) The operation used in step 3 of the above simplification steps is _____. (Fill in "polynomial multiplication" or "factorization")

(3) Please write down the correct solution process for this question, and choose a suitable integer value from $-2 \lt x \lt 2$ to find the value of the fraction.

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