
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 $S_n$ is the sum of the first $n$ terms of the sequence ${a_n}$ and $2S_n = 3a_n - 3 (n \in \mathbb{N}^*)$,

(1) Find the general term formula for the sequence ${a_n}$;

(2) If the general term formula for the sequence ${b_n}$ is ${b_n} = 4n + 1 (n \in \mathbb{N}^*)$, and a new sequence ${c_n}$ is formed by arranging the common terms of the sequences ${a_n}$ and ${b_n}$ in the order they appear in the original sequences, find the sum of the first $n$ terms ($T_n$) of the sequence $\{\frac{1}{\log_9 c_n \log_9 c_{n+2}}\}$.

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