
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 that the sequence $\{a\_n\}$ is an arithmetic sequence with $a\_2=1$ and $a\_5=-5$.

(1) Find the general term $a\_n$;
(2) Find the maximum value of the sum $S\_n$ of the first $n$ terms;
(3) Let $b\_n=\frac{1}{(4-a\_n)(4-a\_{n+1})}$. 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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