
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
Consider an arithmetic sequence $\{a\_n\}$. If $a\_1=2$, $a\_n \neq 0$, and $n a\_{n+1} - a\_n^2 + n a\_{n-1} = 0$ ($n \geqslant 2)$, find $a\_n=$ \_\_\_\_\_\_ and $\frac{S\_{2015}}{2015}=$ \_\_\_\_\_\_.

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