
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 sequence $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$, and $S_n = \frac{3}{2}a_n - 1$ ($n \in \mathbb{N}^*$),
(Ⅰ) Find the general term formula for the sequence $\{a_n\}$;
(Ⅱ) In the sequence $\{b_n\}$, where $b_1=5$, $b_{n+1} = b_n + a_n$, find the sum of the first $n$ terms, $T_n$, of the sequence $\{\log_{9}(b_n-4)\}$.

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