
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
Given a quadratic function $f(x) = ax^2 + kx + c + d$, where $a > 0$, $k \neq b$, and $d$ is a constant, determine the vertex $(x, y)$ of this parabola and calculate $f(x)$ at this vertex.
**A)** $\left(\frac{-k}{2a}, \frac{k^2}{4a} + c + d\right)$\
**B)** $\left(\frac{-k}{2a}, \frac{-k^2}{4a} + c - d\right)$\
**C)** $\left(-\frac{k}{2a}, \frac{-k^2}{4a} + c + d\right)$\
**D)** $\left(\frac{k}{2a}, \frac{-k^2}{4a} + c + d\right)$\
**E)** None of these

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