
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
The following is the process of simplifying fractions by Xiaobai. Please read carefully and complete the corresponding tasks.

Solution: $(\frac{3x+4}{x^2-1}-\frac{2}{x-1})÷\frac{x+2}{x^2-2x+1}$

$=[\frac{3x+4}{(x+1)(x-1)}-\frac{2}{x-1}]÷\frac{x+2}{(x-1)^2}\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $Step 1

$=[\frac{3x+4}{(x+1)(x-1)}-\frac{2(x+1)}{(x+1)(x-1)}]\div \frac{x+2}{(x-1)^{2}}\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $Step 2

$=\frac{3x+4-2x+2}{(x+1)(x-1)}×\frac{(x-1)^2}{x+2}\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $Step 3

$=\frac{x+6}{x+1}×\frac{x-1}{x+2}\ldots \ldots \ldots \ldots \ldots \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

$=\frac{x^2+5x-6}{x^2+3x+2}\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $Step 5

Tasks:

(1) Fill in the blanks:

① In the simplification steps above, the ______ step is to find a common denominator for the fractions, based on the property of ______.

② Errors start to appear in step ______. The reason for the error in this step is ______.

(2) Please write down the correct simplification process.

(3) When $x=2$, find the value of the fraction.

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