
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
Consider an arithmetic series where the first term is $k^2 + k + 1$ and each term increases by 1. Calculate the sum of the first $2k + 3$ terms of this series.
A) $2k^3 + 7k^2 + 10k + 6$
B) $2k^3 + 6k^2 + 9k + 3$
C) $2k^3 + 8k^2 + 11k + 7$
D) $2k^3 + 5k^2 + 8k + 5$

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