
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 function $f(x)=\frac{7x+5}{x+1}$, a sequence $\{a\_n\}$ satisfies $2a_{n+1}-2a_{n}+a_{n+1}a_{n}=0$ and $a_{n}\neq 0$. Another sequence $\{b\_n\}$ is defined as $b_{1}=f(0)$ and $b_{n}=f(a_{n}-1)$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Find the sum $S_{n}$ of the first $n$ terms of the sequence $\{a_{n}a_{n+1}\}$.
3. 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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