
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
In a non-zero common difference arithmetic sequence $\{a\_n\}$, the sum of the first $n$ terms is $S\_n$. It is known that $a\_3=5$, and $a\_1$, $a\_2$, $a\_5$ form a geometric sequence.
(I) Find $a\_n$ and $S\_n$;
(II) Let $T\_n= \frac {1}{a\_1a\_2} + \frac {1}{a\;\_{2}a\_{3}} + … \frac {1}{a\_{n}a\_{n+1}}$, if $T\_n \geqslant \frac {9}{S\_{n+k}}$ holds for any positive integer $n$, find the minimum value of positive integer $k$.

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