
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 its first $n$ terms sum $S_n$, $a_1=3$, and $S_n=na_{n+1}-n^2-n$.
1. Find the general formula for the $n^{th}$ term of the sequence ${a_n}$.
2. If sequence ${b_n}$ satisfies $b_n=\frac{2n+1}{n^2(a_{n+1}-1)^2}$, find the sum of the first $n$ terms, $T_n$, of ${b_n}$.

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