
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 a positive-term geometric sequence $\{a_n\}$ satisfying $a_3a_9=4a_5^2$ and $a_2=1$,
1. Find the general term formula for $\{a_n\}$;
2. Let $b_n = 2na_n$, find the sum of the first $n$ terms of sequence $\{b_n\}$, denoted as $S_n$.

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