
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
Given that the equation about $x$ is $x^{2}+2\left(a-1\right)x+a^{2}-7a-4=0$ with roots $x_{1}$ and $x_{2}$, and it satisfies $x_{1}x_{2}-3x_{1}-3x_{2}-2=0$. Find the value of $(1+\frac{4}{{a}^{2}-4})\cdot \frac{a+2}{a}$.

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