
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 the quadratic equation $ax^2 + bx + c = 0$ to be triple the other, determine the relationship between the coefficients $a, b, c$.
**A)** $4b^2 = 9ac$  
**B)** $b^2 = 12ac$  
**C)** $3b^2 = 16ac$  
**D)** $b^2 - 12ac = 0$  
**E)** $8b^2 = 3ac$

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