
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 $\{a_n\}$ whose first $n$ terms sum $s_n = n^2 + 4n$ ($n \in \mathbb{N}^*$), and a geometric sequence $\{b_n\}$ with the first term $b_1 = 2$ and common ratio $q$ ($q > 0$), it is also known that $b_2$, $b_3 + 4q$, and $b_4$ form an arithmetic sequence.  
(1) Find the general formulas for sequences $\{a_n\}$ and $\{b_n\}$.  
(2) Let $c_n = \frac{3(a_n - 3)b_n}{4} = n \cdot 3^n$, and denote the sum of the first $n$ terms of sequence $\{c_n\}$ as $T_n$, find $T_n$.

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