
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
For one root of a quadratic equation $ax^2 + bx + c = 0$ to be triple of the other, what must the relationship between the coefficients $a,\,b,\,c$ be?
**A)** $3b^2 = 16ac$\
**B)** $3b^2 = 8ac$\
**C)** $4b^2 = 18ac$\
**D)** $b^2 - 12ac = 0$\
**E)** $12b^2 = 3ac$

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