
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
Let $x$ be a real number, and consider the equation $9y^2 - 3xy + x + 8 = 0$. What is the set of all possible values for $x$ such that $y$ is a real number?
A) $x \leq -4 \text{ or } x \geq 8$
B) $x \leq -8 \text{ or } x \geq 4$
C) $-4 \leq x \leq 8$
D) $-8 \leq x \leq 4$
E) $x \leq -8 \text{ or } x \geq -4$

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