
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 $n∈N^{+}$, and the sequence ${a_n}$ satisfies: $a_1=1$, $a_{n+1}= \frac {1}{4}|A\_nB\_n|^2$, find the general term formula for the sequence ${a_n}$.

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