
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
In an arithmetic series where the first term is $k^2 - k + 1$ and the consecutive terms increase by $1$, calculate the sum of the first $2k + 1$ terms.
A) $k^3 + (k + 1)^3$
B) $(2k + 1)(k^2 + 1)$
C) $(k+1)^3 $
D) $(k + 1)^2 $
E) $(2k + 3)(k^2 + 1)^2$

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