
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
A sequence $\{a_n\}$ satisfies the equation $S_n = \frac{3}{2}a_n - \frac{1}{2}a_1$, where $S_n$ is the sum of the first $n$ terms. Also, $a_1, a_2 + 6, a_3$ form an arithmetic sequence.

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

(II) Let $b_n = \frac{a_{n+1}}{S_n S_{n+1}}$, find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$.

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