
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
The function $f(x) = a^x$ passes through the point $(1, \frac{1}{2})$, and the point $\left(n-1, \frac{a_n}{n^2}\right)$ (where $n\in \mathbb{N}^*$) lies on the graph of $f(x) = a^x$.  
(I) Find the general term formula for the sequence $\{a_n\}$.  
(II) Let $b_n= \frac {a_n}{n}$, and suppose the sum of the first $n$ terms of the sequence $\{b_n\}$ is $S_n$. Calculate $S_n$.

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