
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
Solve for \(k\) in the quadratic equation \(3x^2 - (k+2)x + 6 = 0\) such that the equation has real roots and one of the roots is equal to 3.
A) 9
B) -9
C) -6√2 and 6√2
D) All real numbers

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