
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 that the sum of the first $n$ terms of a sequence ${a_n}$ is $S_n$, and $a_2=8$, $S_n=\frac{a_{n+1}}{2}-n-1$.

(1) Find the general term formula of the sequence ${a_n}$.

(2) Find the sum of the first $n$ terms, $T_n$, of the sequence $\{\frac{2\times3^{n}}{a_n\cdot a_{n+1}}\}$.

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