
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 an arithmetic sequence $\{a\_n\}$ with distinct terms, the sum of the first five terms $S\_5=20$. Also, $a\_1$, $a\_3$, and $a\_7$ form a geometric sequence.

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

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