
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 $\{a\_n\}$, its first $n$ terms sum is $S\_n$. The points $(n, S\_n) (n \in \mathbb{N}^*)$ lie on the graph of the function $y = 2x^2 + x$. Determine the general term formula of the sequence $\{a\_n\}$.

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