
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 $a_{10} = 28$, $S\_8 = 92$. Moreover, for any $n$ in the set of positive integers, the product of the first $n$ terms of the sequence \{$b\_n$\} is $3n + 1$.

(1) Find the general term formulas for the sequences \{$a\_n$\} and \{$b\_n$\};

(2) Let $c\_n = \frac{a\_n \cdot b\_n}{2^n}$. Find the sum of the first $n$ terms of the sequence \{$c\_n$\}, denoted as $T\_n$.

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