
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
In the arithmetic sequence $\{a_n\}$, $a_2=5$, $a_5=11$, the sum of the first $n$ terms of the sequence $\{b_n\}$ is $S_n=n^2+a_n$.

(Ⅰ) Find the general formula for the sequences $\{a_n\}$ and $\{b_n\}$;

(Ⅱ) Find the sum of the first $n$ terms, $T_n$, of the sequence $\left\{ \frac{1}{{b_n}{b_{n+1}}} \right\}$.

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