
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 $\{a_n\}$ where $S_n$ represents the sum of the first $n$ terms of the sequence, it is known that $a_1 = 1$ and $S_{n+1} = 3S_n + 2$ for $n \in \mathbb{N}$.  
(1) Find the general term formula for the sequence $\{a_n\}$.  
(2) If $b_n = \frac{8n}{a_{n+1} - a_n}$, find the sum $T_n$ of the first $n$ terms of the sequence $\{b_n\}$.

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