
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
Consider an arithmetic sequence $\{a_{n}\}$ where $a_{3} + a_{4} = 4$ and $a_{5} + a_{7} = 6$.
(I) Find the general term formula for $\{a_{n}\}$;
(II) Let $b_{n} = a_{n} \cdot 5^{n}$, find the sum of the first $n$ terms of $\{b_{n}\}$, denoted as $S_{n}$.

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