
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
Suppose \(x\) is real and \(3y^2 + 2xy + x + 5 = 0\). Find all values of \(x\) for which \(y\) is real.
A) \(x > 5 \text{ or } x < -3\)
B) \(x \geq -3 \text{ or } x \leq 5\)
C) \(x \leq -3 \text{ or } x \geq 5\)
D) all real numbers
E) no real values of \(x\)

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