
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 progression, and $\frac{3}{2}$, $3$, $a\_4$, $a\_{10}$ form a geometric progression.
(I) Find $a\_n$;
(II) Find the sum of the first $n$ terms, $S\_n$, of the sequence $\{ \frac{2}{a\_n(a\_n+n)}\}$.

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