
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 $\{a_n\}$, where $a_n=\begin{cases}n+1, & n\leqslant 7 \\ n-1, & n > 7\end{cases}$ $(n\in\mathbb{N}^*)$.  
(1) Determine whether the sequence $\{a_n\}$ is an arithmetic sequence;  
(2) Find the sum of the first $n$ terms of the sequence $\{a_n\}$, denoted as $S_n$.

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