
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 the sequence $\left\{u_{n}\right\}$ with the sum of the first $n$ terms denoted as $S_{n}$. If $S_{1}=1$ and $S_{n+1}-S_{n}+(5n+1) a^{n}, n=1,2,3, \cdots (|a| \neq 1)$, find $S_{n}$.

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