
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
In an arithmetic sequence $\{a_n\}$ where all terms are distinct, it is known that $a_4=5$, and $a_3$, $a_5$, $a_8$ form a geometric sequence.  
(1) Find $a_n$;  
(2) Let the sum of the first $n$ terms of the sequence $\{a_n\}$ be $S_n$, and let $b_n= \frac{n+3}{2a_n\cdot S_n}$. 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