
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 $a\_1=1$ and $a\_4=8$, and $\{b\_n\}$ is an arithmetic sequence with $b\_1=3$ and $b\_4=12$,

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

(2) Let $c\_n = a\_n + b\_n$, find the sum of the first $n$ terms of the sequence $\{c\_n\}$, denoted as $S\_n$.

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