
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 sum of the first $n$ terms of the sequence ${a_n}$ is $S_n$, and the points $(n, S_n)$ all lie on the graph of the function $y = \frac{3}{2}x^2 - \frac{1}{2}x$.

1. Find the general term formula for the sequence ${a_n}$.
2. Let ${b_n} = \frac{3}{{a_n}{a_{n+1}}}$, and ${T_n}$ be the sum of the first $n$ terms of the sequence ${b_n}$. Find the smallest positive integer $m$ such that ${T_n} < \frac{m}{20}$ holds for all $n \in \mathbb{N}^+$.

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