
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 $a\_1=0$. For any $n∈N^{*}$, we have $na_{n+1}=S_{n}+n(n+1)$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. If the sequence $\{b\_n\}$ satisfies $a_{n}+log _{2}n=log _{2}b_{n}$, find the sum of the first $n$ terms of the sequence $\{b\_n\}$, denoted as $T_{n}$.

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