
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: $\frac{a^{2}+a}{a^{2}-3a}\div \frac{a^{2}-1}{a-3}-\frac{1}{a+1}$, where $a=-2$.<br/>$(2)$ Given the fraction $\frac{x^{2}-1}{x-4}$, please choose one from the fractions $\frac{x+1}{4-x}$ and $\frac{4x-1}{x-4}$, and choose an operation to make their result an integer polynomial.<br/>$I$. I choose ________$(fill in the number)$;<br/>$II$. Write down the expression and calculate.

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