
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 $\left\{ a_n \right\}$ with the sum of the first $n$ terms denoted as $S_n$, and $S_n=\frac{3}{2}a_n-\frac{1}{2}$,

(1) Find the general formula for the sequence $\left\{ a_n \right\}$;

(2) If $b_n=\frac{2n}{a_{n+2}-a_{n+1}}$, find the sum of the first $n$ terms of the sequence $\left\{ b_n \right\}$, denoted as $T_n$.

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