
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]


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Below is the process of simplifying a fraction by Xiao Ming. Please read carefully and complete the corresponding tasks.<br/>$\frac{x^2-9}{x^2+6x+9}-\frac{2x+1}{2x+6}$,<br/>$=\frac{(x+3)(x-3)}{(x+3)^{2}}-\frac{2x+1}{2(x+3)}\ldots $Step 1,<br/>$=\frac{x-3}{x+3}-\frac{2x+1}{2(x+3)}\ldots $Step 2,<br/>$=\frac{2x-3}{2(x+3)}-\frac{2x+1}{2(x+3)}\ldots $Step 3,<br/>$=\frac{2x-6-(2x+1)}{2(x+3)}\ldots $Step 4,<br/>$=\frac{2x-6-2x+1}{2(x+3)}\ldots $Step 5,<br/>$=-\frac{5}{2x+6}\ldots $Step 6.<br/>Task 1: Fill in the blanks:<br/>① In the above simplification steps, the ______ step is to find a common denominator for the fractions. The basis for finding a common denominator is ______ or can be filled in as: ______;<br/>② Errors start to appear in the ______ step. The reason for this error is ______;<br/>Task 2: Please write down the correct result of the simplified fraction, which is ______;<br/>Task 3: According to Xiao Ming's process of simplifying fractions, complete the following calculation: $\frac{1}{\;a+1}-\frac{a+2}{{a}^{2}-1}•\frac{{a}^{2}-2a+1}{{a}^{2}+4a+4}$.

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