
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 the sequence $\{a\_n\}$ satisfies $a\_1=1$, and $a_{n+1}=2a\_n$, set $b\_n-2=3\log \_{2}a\_n (n∈N\_+)$.
(I) Find the general term formula for the sequence $\{b\_n\}$;
(II) Find the sum of the first $n$ terms, $S\_n$, of the sequence $\{|a\_n-b\_n|\}$.

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