
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 sequence $\{a\_n\}$ with positive terms, its sum of the first $n$ terms is $T\_n$, $a\_1=2$, and $a\_n a_{n+1} = 6T_n - 2$.
(I) Find the general term formula for the sequence $\{a\_n\}$;
(II) If $b\_n = 2^n$, find the sum of the first $n$ terms, $S\_n$, for the sequence $\{|a\_n - b\_n|\}$.

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