
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
Given a sequence \(\left\{u_{n}\right\}\) defined by \(u_{1}=5\) and \(u_{n+1}-u_{n}=3+4(n-1)\) for \(n=1,2,3, \ldots\), find the sum of the coefficients of the polynomial representing \(u_{n}\).

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