
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]


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The sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$ is $S_n$. It is known that for any $n \in \mathbb{N}^*$, the point $(n, S_n)$ lies on the graph of the quadratic function $f(x) = x^2 + c$. Find the values of $c$ and $a_n$.

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