
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
If a one-variable quadratic equation about $x$ is $ax^{2}+bx+c=0$ and has two real roots, with one root being twice the other, then this equation is called a "double root equation." <br/> $(1)$ Is the one-variable quadratic equation $x^{2}-3x+2=0$ a double root equation? If so, please explain the reason. <br/> $(2)$ If the one-variable quadratic equation $ax^{2}+bx-6=0$ is a double root equation and the equation has one root as $2$, find the values of $a$ and $b$.

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