
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 the sequence $\left\{u_n\right\}$ defined by $u_1=5$ and $u_{n+1}-u_n=3+4(n-1)$ for $n=1,2,3,\ldots$. If $u_n$ can be expressed as a polynomial in $n$, find the algebraic sum of the coefficients of this polynomial.

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