
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 sum of the first $n$ terms of the arithmetic sequence $\{a\_n\}$ is $S\_n$, and $a\_3=7$, $S\_4=24$. The sum of the first $n$ terms of the sequence $\{b\_n\}$ is $T\_n=n^2+a\_n$.

1. Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$.
2. Find the sum of the first $n$ terms of the sequence $\{\frac{b\_n}{2^n}\}$, denoted as $B\_n$.

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