
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 geometric sequence $\{a_n\}$ satisfies $a_2 + a_3 + a_4 = 28$, and $a_3 + 2$ is the arithmetic mean of $a_2$ and $a_4$. If $b_n = 2^{2n+1}$, the sum of the first $n$ terms of sequence $\{b_n\}$, denoted as $S_n$, is $\boxed{\text{\_\_\_\_\_\_}}$.

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