
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, and its derivative $f'(x)=6x-2$. The sequence $\{a_n\}$ has a sum of the first $n$ terms denoted by $S_n$. The points $(n, S_n)$ (where $n \in \mathbb{N}^*)$ all lie on the graph of $y=f(x)$.
1. Find the general term 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 $\{b_n\}$. Find the range of values for $m$ such that $T_n \geq \frac{m}{20}$ for all $n \in \mathbb{N}^*$.

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