
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 sequence $\{a_n\}$ is an arithmetic sequence with a non-zero common difference, $a_1=2$, and $a_2$, $a_3$, $a_4+1$ form a geometric sequence.
(I) Find the general term formula for the sequence $\{a_n\}$;
(II) Let $b_n=\frac{2}{n\cdot(a_n+2)}$, find the sum $S_n$ of the first $n$ terms of the sequence $\{b_n\}$.

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