
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 teacher assigned exercises from the textbook as homework today: Calculate $(\frac{3x}{x-2}-\frac{x}{x+2})⋅\frac{x^2-4}{x}$ using two methods. Below is part of Xiao Li's homework operation process:  
Solution: Original expression $=[\frac{3x(x+2)}{(x-2)(x+2)}-\frac{x(x-2)}{(x-2)(x+2)}]•\frac{{x}^{2}-4}{x}\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $ Step 1  
$=[\frac{3x^2+6x}{(x-2)(x+2)}-\frac{x^2-2x}{(x-2)(x+2)}]⋅\frac{(x+2)(x-2)}{x}\ldots \ldots \ldots $ Step 2  
$=\frac{3x^2+6x(x^2-2x)}{(x-2)(x+2)}⋅\frac{(x+2)(x-2)}{x}\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $ Step 3  
$=\frac{3{x}^{2}+6x-{x}^{2}-2x}{(x-2)(x+2)}•\frac{(x+2)(x-2)}{x}\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $ Step 4  
$=\ldots \ldots $  
$(1)$ In the above simplification steps, the ______ step is to find a common denominator;  
$(2)$ Errors start to appear in step ______, the reason for the error is ______;  
$(3)$ Simplify the expression using the second method.

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