
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 $\{a_n\}$ be a sequence where the sum of the first $n$ terms is denoted as $S_n$, and the point $(n,S_n)$ lies on the curve of the function $y= \frac{3}{2}x^2- \frac{1}{2}x$.
(1) Find the general formula for the sequence $\{a_n\}$.
(2) Let $b_n= \frac{3}{a_na_{n+1}}$, and let $T_n$ be the sum of the first $n$ terms of the sequence $\{b_n\}$. Determine the smallest integer $m$ such that $T_n < \frac{m}{20}$ holds for all positive integers $n$.

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