
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 geometric sequence $\{a_n\}$ where all terms are positive, $a_1=2$, and $2a_1, a_3, 3a_2$ form an arithmetic sequence.  
(1) Find the general term formula for the sequence $\{a_n\}$.  
(2) Let $S_n$ be the sum of the first $n$ terms of $\{a_n\}$, and define $b_n = \frac{a_{n+1}}{S_nS_{n+1}}$. Find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted $T_n$.

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