
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 line $l\_n$: $y=x- \sqrt {2n}$ and the circle $C\_n$: $x^{2}+y^{2}=2a\_n+n$ intersect at two distinct points $A\_n$, $B\_n$, where $n∈N^{}$. The sequence ${a_n}$ satisfies: $a_1=1$, $a_{n+1}= \frac {1}{4}|A_nB_n|^{2}$.
(I) Find the general term formula $a_n$ for the sequence ${a_n}$;
(II) If $b_n= \frac {n}{4a_n}$, find the sum $T_n$ of the first $n$ terms of the sequence ${b_n}$.

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