
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
Suppose the sequence $\{a\_n\}$ is an increasing arithmetic sequence, where $a\_3=5$, and $a\_1$, $a\_2$, $a\_5$ form a geometric sequence,
(1) Find the general term formula for $\{a\_n\}$;
(2) Let $b\_n=\frac{1}{(a\_n+1)(a_{n+1}+1)}$, find the sum of the first $n$ terms, $T\_n$, of the sequence $\{b\_n\}$.

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