
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 $\{u_n\}$ be defined by $u_1=4$ and the recurrence relation $u_{n+1}-u_n=2n^2 - 2n + 1, n=1,2,3,\dots$. If $u_n$ is expressed as a polynomial in $n$, find the algebraic sum of its coefficients.

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