
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 $ax^2 + bx + c = 0$ to be three times the other, and the coefficient $b$ to equal $6$, find the condition relating coefficients $a$ and $c$.
A) $c = \frac{27}{4a}$
B) $c = \frac{9}{2a}$
C) $c = \frac{4a}{27}$
D) $c = \frac{2a}{9}$

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