
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]


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Given that the geometric sequence $\{a_n\}$ consists of positive terms, with $a_2 = 4$ and $a_3 + a_4 = 24$.

(Ⅰ) Find the general term formula for the sequence $\{a_n\}$.

(Ⅱ) Suppose the sequence $\{b_n\}$ satisfies $b_1 = 3$, $b_2 = 6$, and the sequence $\{b_n - a_n\}$ forms an arithmetic sequence, calculate the sum of the first $n$ terms of the sequence $\{b_n\}$.

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