
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
Let $\{a\_n\}$ be an arithmetic sequence with a non-zero common difference. The sum of its first $n$ terms is denoted by $S\_n$. Given that $S\_9=90$, and $a\_1$, $a\_2$, $a\_4$ form a geometric sequence.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Let $b\_n=\frac{1}{a\_n a\_{n+1}}$, find the sum of the first $n$ terms of the sequence $\{b\_n\}$, denoted by $T\_n$.

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