
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 first $n$ terms sum $S_{n}$ satisfying $2 S_{n}-n a_{n}=n \left( n \in \mathbf{Z}_{+} \right)$, and $a_{2}=3$,
(1) Find the general term formula for the sequence $\left\{a_{n}\right\}$;
(2) Given another sequence $\left\{b_{n}\right\}$ with the first $n$ terms sum, find the minimum positive integer $n$ such that $T_{n}>\frac{9}{20}$.

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