
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 smallest integral value of \( k \) such that the quadratic equation
\[ (k+1)x^2 - (6k+2)x + 3k + 2 = 0 \]
has no real roots.
- A) 0
- B) 1
- C) 2
- D) 3

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