
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 $v_{n+1}-v_n=5+6(n-1), n=1,2,3\cdots.$ Express $v_n$ as a polynomial in $n$ and find the algebraic sum of its coefficients.

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