
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 sequences $\{a\_n\}$ and $\{b\_n\}$, if $a\_1=3$ and for any positive integer $n$, $a\_{n+1}-a\_n=2$, and the sum of the first $n$ terms of the sequence $\{b\_n\}$ is $S\_n=n^{2}+a\_n$.
(I) Find the general terms of the sequences $\{a\_n\}$ and $\{b\_n\}$;
(II) Find the sum of the first $n$ terms, $T\_n$, of the sequence $\{\frac{1}{b\_nb\_{n+1}}\}$.

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