
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 $\{a\_n\}$ is an arithmetic sequence, and $a\_2=3$, the sum of the first 4 terms of $\{a\_n\}$ is 16, and the sequence $\{b\_n\}$ satisfies $b\_1=4$, $b\_4=88$, and $\{b\_n\-a\_n\}$ is a geometric sequence.
(Ⅰ) Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\-a\_n\}$;
(Ⅱ) Find the sum $S\_n$ of the first $n$ terms of the sequence $\{b\_n\}$.

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