
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
Let the sequence $\{a_n\}$ have a sum of the first $n$ terms denoted as $S_n$, with $a_1=1$ and $S_n =na_n -3n(n-1)$, where $(n\in\mathbb{N}^*)$.

(Ⅰ) Find the general formula for $a_n$;

(Ⅱ) Determine whether there exists 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 it exists, find the value of $n$; if not, explain why.

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