
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 $u_1 = 6$ and the relationship $u_{n+1} - u_n = 5 + 2(n-1), n = 1, 2, 3, \cdots.$ Express $u_n$ as a polynomial in $n$ and calculate the algebraic sum of its coefficients.

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