
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 $y=f(x)$ whose graph passes through the origin, its derivative is $f′(x)=6x-2$. The sum of the first $n$ terms of the sequence ${a_n}$ is $S_n$, and the points $(n,S_n)(n∈N^{*})$ all lie on the graph of the function $y=f(x)$.
(I) Find the general term formula for the sequence ${a_n}$;
(II) Let $b_{n}= \frac {3}{a_{n}a_{n+1}}$, $T_{n}$ is the sum of the first $n$ terms of the sequence ${b_{n}}$, find the smallest positive integer $m$ such that $T_{n} < \frac {m}{20}$ holds for all $n∈N^{*}$.

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