
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
Suppose $A_{n}$ and $B_{n}$ represent the sum of the first $n$ terms of the sequences $\{a_{n}\}$ and $\{b_{n}\}$ respectively. For any positive integer $n$, $a_{n}=2(n+1)$, $B_{n}=n^{2}+5n$.

1. Find the general term formula for the sequence $\{b_{n}\}$.
2. Let $\{c_{n}=\frac{2}{A_{n}-2n}\}$, find the sum of the first $n$ terms of the sequence $\{c_{n}\}$, denoted as $S_{n}$.

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