
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 the sum of the first $n$ terms of the sequence ${a_n}$ is $S_n=a_n+n^2-1$, and the sequence ${b_n}$ satisfies $3^{n}⋅b_{n+1}=(n+1)a_{n+1}-na_{n}$, with $b_{1}=3$.
(I) Find $a_n$ and $b_n$;
(II) Let $T_{n}$ be the sum of the first $n$ terms of the sequence ${b_n}$, find $T_{n}$, and find the maximum value of $n$ such that $T_{n} < 7$.

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