
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 common difference of the arithmetic sequence $\{a_n\}$ is 2, and $a_1$, $a_1+a_2$, $2(a_1+a_4)$ form a geometric sequence. Find the sum $S_n$ of the first $n$ terms of the sequence $\{\frac{a_n}{2^{n-1}}\}$.

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