
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
When solving a quadratic equation, there is a method called the "average method." For example, when solving the equation $x(x+8)=4$, the solution process is as follows:

Given equation: $x(x+8)=4$

Solution: The original equation can be transformed to get $[(x+4)-4][(x+4)+4]=4$

$(x+4)^2-4^2=4$

$(x+4)^2=20$

Taking the square root directly, we get $x_{1}=-4+2\sqrt{5}$, $x_{2}=-4-2\sqrt{5}$.

$(1)$ Below is the solution process written by Xiao Ming using the "average method" to solve the equation $(x+2)(x+8)=40$:

Solution: The original equation can be transformed to get $[(x+a)-b][(x+a)+b]=40$

$(x+a)^2-b^2=40$

$(x+a)^2=40+b^2$

Taking the square root directly, we get $x_{1}=c$, $x_{2}=d$.

In the above solution process, the numbers represented by $a$, $b$, $c$, $d$ are ______, ______, ______, ______.

$(2)$ Please use the "average method" to solve the equation: $(x-2)(x+6)=4$.

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