
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
Is the quadratic equation $x^2 - 3x + 2 = 0$ a "root-multiplying equation" that has two real number roots, such that one root is twice the other?  
(1) Please determine whether $x^2 - 3x + 2 = 0$ is a root-multiplying equation, and if it is, provide the reasoning.  
(2) If $ax^2 + bx - 6 = 0$ is a root-multiplying equation with one root being 2, find the values of $a$ and $b$.

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