
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
We define: If a quadratic equation in $x$, $ax^{2}+bx+c=0$, has two real roots, and one root is twice the other, then we call such an equation a "double root equation".  
$(1)$ Please determine whether the equation $x^{2}-6x+8=0$ is a double root equation, and explain the reason;  
$(2)$ If $\left(x-8\right)\left(x-n\right)=0$ is a double root equation, then $n=\_\_\_\_\_\_.$

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