
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 a sequence \( \{v_n\} \) be defined by \( v_1 = 7 \) and the relationship \( v_{n+1} - v_n = 5 + 3(n-1), n=1,2,3,\cdots \). If \( v_n \) is expressed as a polynomial in \( n \), what is the algebraic sum of its coefficients?
A) 3
B) 5
C) 7
D) 9
E) 11

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