
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 $\{a\_n\}$ is a geometric sequence with $a\_1=3$ and $a\_4=24$, and the sequence $\{a\_n + b\_n\}$ is an arithmetic sequence with first term $4$ and common difference $1$.

1. Find the general term formulas for $\{a\_n\}$ and $\{b\_n\}$.
2. Calculate the sum of the first $n$ terms for $\{b\_n\}$.

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