
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 the sequence ${a_n}$ where $a_1=1$ and $a_n-a_{n-1}+1=2n$ for $n\in\mathbb{N^*}$, $n\geq 2$.
(I) Find the general term formula for the sequence ${a_n}$.
(II) If $b_n=\frac{1}{4a_n-1}$, find the general term formula for the sequence ${b_n}$ and the sum of its first $n$ terms, $T_n$.

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