
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
Let the sequence $\{v_n\}$ be defined by $v_1 = 5$ and the recurrence relationship for the sequence given as follows: $v_{n+1}-v_n = n^2 + n - 1$, for $n = 1, 2, 3 \cdots$. If $v_n$ is expressed as a polynomial in $n$, the algebraic sum of its coefficients is:
A) 2
B) 3
C) 4
D) 5
E) 6

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