
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
Consider an arithmetic sequence $\{a\_n\}$ with a common difference not equal to zero, where the sum of the first $n$ terms is denoted as $S\_n$. Given that $a\_1=2$ and $a\_4$ is the geometric mean of $a\_2$ and $a\_8$.
(I) Find the general term formula for the sequence $\{a\_n\}$.
(II) Find the sum of the first $n$ terms, $T\_n$, for the sequence $\{ \frac{1}{S\_n} \}$.

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