
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 an arithmetic sequence $\{a_{n}\}$ that satisfies $a_{1}+a_{2}=3$, $a_{4}-a_{3}=1$. Let $\{b_{n}\}$ be a geometric sequence where $b_{2}=a_{4}$, $b_{3}=a_{8}$.
(I) Find the general terms of the sequences $\{a_{n}\}$ and $\{b_{n}\}$.
(II) Let $c_{n}=a_{n}+b_{n}$, find the sum of the first $n$ terms, $S_{n}$, of the sequence $\{c_{n}\}$.

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