
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
It is known that the sequence $\{b_n\}$ is a geometric sequence, with $b_n = 2^{a_n - 1}$, and the terms $a_1 = 2$, $a_3 = 4$.
(1) Find the general formula for the sequence $\{a_n\}$;
(2) Find the sum of the first $n$ terms $S_n$ for the sequence $\left\{ \frac{a_n}{b_n} \right\}$.

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