
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
The first term of an arithmetic series of consecutive integers is $(k^2 - k + 1)$. Calculate the sum of the first $k + 2$ terms of this series.
**A)** $k^3 + \frac{3k^2}{2}$
**B)** $k^3 + k^2 + k$
**C)** $(k+2)(k^2 - k +1)$
**D)** $k^3 + \frac{3k^2}{2} + \frac{k}{2} + 2$

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