
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 sequence ${a_n}$ is an arithmetic sequence with $a_5=14$ and $a_7=20$. The sum of the first $n$ terms of the sequence ${b_n}$ is $S_n$, where $b_1=\frac{2}{3}$ and $3S_n = S_{n-1} + 2$ for $n \geq 2, n \in N$.

(I) Find the general term formulas for the sequences ${a_n}$ and ${b_n}$;
(II) If $c_n = a_n \cdot b_n$, for $n = 1, 2, 3, ...$, and $T_n$ represents the sum of the first $n$ terms of the sequence ${c_n}$, find the smallest value of $m$ such that $T_n < m$ holds true for all $n \in N^*$.

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