
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 first term of a sequence $\{a_n\}$ is $1$, and the sum of the first $n$ terms is denoted as $S_n$. If the points $(S_{n-1}, a_n)$ ($n \geq 2$) are on the graph of the function $y = 3x + 4$.

(I) Find the general term formula of the sequence $\{a_n\}$.

(II) If $b_n = \log_2 \frac{a_{n+2}}{7}$, and $b_n = 2^{n+1} \cdot c_n$, where $n \in \mathbb{N}^*$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, denoted as $T_n$.

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