
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
$(1)$ Factorization: $m^{3}-4m^{2}+4m$;<br/>$(2)$ After learning about fraction operations, the teacher assigned the following calculation problem: $\frac{2}{x^{2}-1}-\frac{1}{x-1}$. Xiao Ming's solution process is as follows: $\frac{2}{x^{2}-1}-\frac{1}{x-1}=\frac{2}{(x+1)(x-1)}-\frac{1}{x-1}$①<br/>$=\frac{2}{(x+1)(x-1)}-\frac{x+1}{(x+1)(x-1)}$②<br/>$=2-\left(x+1\right)$③<br/>$=1-x$④<br/>$(1)$ Please analyze Xiao Ming's solution and identify the step where the error occurs (fill in the number), the reason for the error is _______;<br/>$(2)$ Please provide the correct solution process.

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