
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
Xiao Ming simplified $({\frac{{3x+2}}{{x+1}}-2})÷\frac{x}{{{x^2}-1}}$ as follows:<br/>Original expression $=\frac{{3x+2-2x+2}}{{x+1}}÷\frac{x}{{({x+1})({x-1})}}$①,<br/>$=\frac{{x+4}}{{x+1}}⋅\frac{{({x+1})({x-1})}}{x}$②,<br/>$=\frac{{({x+4})({x-1})}}{x}$③.<br/>Please complete the following questions:<br/>$(1)$ Xiao Ming made a mistake starting from step ______ (fill in the step number); the correct simplified result is ______.<br/>$(2)$ When $x=\sqrt{16}-{({\frac{1}{4}})^{-1}}-{({π-3})^0}$, find the value of $({\frac{{3x+2}}{{x+1}}-2})÷\frac{x}{{{x^2}-1}}$.

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