
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 that the sequence $\{a_n\}$ is a geometric sequence with first term $a_1=1$ and common ratio $q=2$, and $\{b_n\}$ is an arithmetic sequence with first term $1$ and common difference $d=2$,
1. Find the general term formula for both sequences $\{a_n\}$ and $\{b_n\}$;
2. Find the sum of the first $n$ terms, denoted as $S_n$, for the sequence $\{\frac{b_n}{2a_n}\}$.

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