
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 the sequence $\{a_n\}$, $a_1=1$ and $a_{n+1}=\frac{2a_n}{2+a_n}$.
(I) Find $a_2$, $a_3$, and $a_4$.
(II) Find the general term formula for the sequence $\{a_n\}$.
(III) If the sequence $b_n=\frac{a_n}{n}$, find the sum of the first $n$ terms, $S_n$, for the sequence $\{b_n\}$.

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