
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 quadratic function $f(x)=ax^2+bx (a \neq 0)$, its derivative is $f'(x)=6x-2$. The sum of the first $n$ terms of the sequence $\{a_n\}$ is denoted as $S_n$, and the points $\{n, S_n\} (n \in \mathbb{N}^*)$ all lie on the graph of the function $y=f(x)$.

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

(2) Let $b_n = \frac{3}{a_n a_{n+1}}$, and let $T_n$ be the sum of the first $n$ terms of the sequence $\{b_n\}$. Find the smallest positive integer $m$ such that $T_n < \frac{m}{2016}$ holds for all $n \in \mathbb{N}^*$.

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