
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
A student simplified the expression $\left(\frac{{x+1}}{{x^2-4}}-\frac{1}{{x+2}}\right) \div \frac{3}{{x-2}}$ as shown below:

解:原式$=[\frac{x+1}{(x+2)(x-2)}-\frac{1}{x+2}]\times \frac{x-2}{3}$①  
$=[\frac{x+1}{(x+2)(x-2)}-\frac{x-2}{(x+2)(x-2)}]\times \frac{x-2}{3}$②  
$=\frac{x+1-x-2}{(x+2)(x-2)}\times \frac{x-2}{3}$③  
$\ldots $

$(1)$上面的运算过程中第______步出现了错误；  
$(2)$请你写出完整的解答过程.

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