
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
If $x$ is real and $4y^2 - 2xy + 2x + 9 = 0$, then the complete set of values of $x$ for which $y$ is real, is:
A) $x \leq -3 \text{ or } x \geq 12$
B) $x \leq -12 \text{ or } x \geq 3$
C) $x \leq -12 \text{ or } x \geq 12$
D) $-3 \leq x \leq 12$
E) $-12 \leq x \leq 3$

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