
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
Determine the value of \( x \) for which the equation \( 4y^2 + y + 6 = 3(9x^2 + y + 3) \) holds true if \( y = 3x \).
A) \( x = 1 \)
B) \( x = -\frac{1}{3} \)
C) \( x = 0 \)
D) \( x = 1 \text{ and } x = -\frac{1}{3} \)

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