
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 a sequence ${a_n}$ is $S_n$ ($n \in \mathbb{N}^*$), and $S_n = \frac{n+2}{3}a_n$, with $a_1 = 1$. Also, ${b_n}$ is a geometric sequence with $b_1 = a_3 - 4$ and $b_4 = a_5 + 1$.

1. Find the general term formulas for ${a_n}$ and ${b_n}$.
2. Let $c_n = \frac{n \cdot b_n}{a_{n+1}}$ ($n \in \mathbb{N}^*$), and the sum of the first $n$ terms of the sequence ${c_n}$ is $T_n$. If $T_n > \frac{m}{2019}$ holds for all $n \in \mathbb{N}^*$, find the maximum value of the integer $m$.

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