
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 $\{a_n\}$ with the sum of its first $n$ terms denoted as $S_n$, and $a_2=8$, $S_n=\frac{a_{n+1}}{2}-n-1$.

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

(2) Find the sum of the first $n$ terms, $T_n$, for the sequence $\left\{ \frac{2\times 3^n}{a_na_{n+1}} \right\}$.

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