
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
Define a sequence \( \{u_n\} \) such that \( u_1=7 \) and the relationship \( u_{n+1}-u_n = 5n + 2(n-1) \) for \( n=1,2,3,\ldots \). Express \( u_n \) as a polynomial in \( n \) and determine the algebraic sum of its coefficients.

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