
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 sequence $\{a_n\}$ is an arithmetic sequence, where $(a_2 + a_3 = 8, a_5 = 3a_2)$.

(1) Find the general term formula for the sequence $\{a_n\}$.

(2) Let $b_n = \frac{2}{a_n a_{n+1}}$, and denote the sum of the first $n$ terms of $\{b_n\}$ as $S_n$. Find the smallest positive integer $n$ such that $S_n > \frac{2016}{2017}$.

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