
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 function $f(x) = 4^x$, suppose the sequence $4, f(a_1), f(a_2), \dots, f(a_n), 2^{n+3}$ ($n \in \mathbb{N}^*$) forms a geometric progression.  
(I) Find the general formula for the sequence ${a_n}$.  
(II) Let $b_n$ be defined as follows:
$$
b_n =
    \begin{cases}
    \frac{1}{n}, &\text{if } n \text{ is even},\\
    n+2,& \text{if } n \text{ is odd},
    \end{cases}
$$
find the sum of the first $n$ terms, denoted as $S_n$, of the sequence $ \left\{ \frac{b_n}{a_n} \right\} $.

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