
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 for what real values of $k$, if any, does the equation $x^2 + (k+1)x + (k^2 - 3) = 0$ have real roots.
A) $k \geq 0$
B) $k < -1$
C) $\frac{1 - 2\sqrt{10}}{3} \leq k \leq \frac{1 + 2\sqrt{10}}{3}$
D) No real values of $k$
E) All real values of $k$

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