
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 common difference $d$ of the arithmetic sequence $\{a_n\}$ is greater than 0, and $a_2$, $a_5$ are the two roots of the equation $x^2 - 12x + 27 = 0$, the sum of the first $n$ terms of the sequence $\{b_n\}$ is denoted as $S_n$, and it is given that $S_n = \frac{3}{2}(b_n - 1)$, for $n \in \mathbb{N}^+$.  
(1) Find the general formula for the sequences $\{a_n\}$ and $\{b_n\}$.  
(2) If $c_n = a_n \cdot b_n$, find the sum of the first $n$ terms $T_n$ of the sequence $\{c_n\}$.

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