
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 the arithmetic sequence $\{a\_n\}$, where $a\_3=9$ and $a\_8=29$.

(I) Find the general term formula for the sequence and the expression for the sum of the first $n$ terms, $S\_n$.

(II) Let $T\_n$ denote the sum of the first $n$ terms of the sequence $\{ \frac{1}{a\_na\_{n+1}} \}$. Find the value of $T\_{100}$.

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