
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 a sequence $\{a_n\}$ where $a_1=2$, $a_2=6$, and the sequence $\{a_{n-1}-a_n\}_{n\in\mathbb{N}^*}$ is an arithmetic sequence with a common difference of $2$.  
(I) Find the general formula for $\{a_n\}$.  
(II) Let the sum of the first $n$ terms of the sequence $\left\{ \frac{1}{a_n} \right\}$ be $S_n$. Find the minimum value of $n$ that satisfies the inequality $S_n > \frac{2015}{2016}$.

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