
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 that the sum of the first $n$ terms of the sequence $\{a\_n\}$ is $S\_n$, and $a\_1=1$, $S\_n=na\_n-3n(n-1),(n∈N^{})$:
-(I) Find the general term formula $a\_n$ of the sequence $\{a\_n\}$;
-(II) Does there exist a positive integer $n$ such that $\frac{S\_1}{1} + \frac{S\_2}{2} + \frac{S\_3}{3} + ... + \frac{S\_n}{n} - \frac{3}{2}(n-1)^2 = 2016$? If so, find the value of $n$; if not, explain why.

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