
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
$(1)$ Simplify first, then find the value: $\frac{{a^2+a}}{{a^2-3a}}÷\frac{{a^2-1}}{{a-3}}-\frac{1}{{a+1}}$, where $a=-2$.<br/>$(2)$ Given the fraction $\frac{{x^2-1}}{{x-4}}$, please choose one of the following fractions and a method of operation to make their result an integer polynomial:<br/>① $\frac{{x+1}}{{4-x}}$;<br/>② $\frac{{4x-1}}{{x-4}}$.<br/>$Ⅰ$. I choose ______$(fill in the number)$.<br/>$Ⅱ$. Write out the expression and calculate.

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