
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 $S_{n}$ is the sum of the first $n$ terms of the sequence $\{a_{n}\}$, $a_{1}=1$, and $na_{n}-S_{n}=n^{2}-n$, where $n\in N^{*}$.<br/>$(1)$ Find the general formula for the sequence $\{a_{n}\}$;<br/>$(2)$ If $b_{n}=\frac{{{2^{{a_n}}}}}{{({{2^{{a_n}}}-1})({{2^{{a_{n+1}}}}-1})}}$, find the sum of the first $n$ terms $T_{n}$ of the sequence $\{b_{n}\}$.

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