
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 the sequence $\left\{a_{n}\right\}$ which satisfies $a_{1}=4$ and $a_{n+1} a_{n}+6 a_{n+1}-4 a_{n}-8=0$, and defining $b_{n}=\frac{6}{a_{n}-2}$ for $n \in \mathbf{N}^{*}$:

(1) Find the general term formula for the sequence $\left\{b_{n}\right\}$.

(2) Find the sum of the first $n$ terms $S_{n}$ of the sequence $\left\{a_{n} \cdot b_{n}\right\}$.

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