
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 the sequence $\{a\_n\}$ is an arithmetic sequence, $S\_n$ is the sum of the first $n$ terms of $\{a\_n\}$, and $a\_10=28$, $S\_8=92$; for any $n∈N^∗$, the sequence $\{b\_n\}$ always satisfies $b\_1⋅b\_2⋅b\_3…b\_n−1⋅b\_n=3n+1$.
(I) Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$;
(II) Let $c\_n=\frac{a\_n \cdot b\_n}{2^n}$, find the sum of the first $n$ terms $T\_n$ for the sequence $\{c\_n\}$.

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