
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 a non-zero common difference arithmetic sequence $\{a_{n}\}$ that satisfies $a_{6}=14$, and $a_{1}$, $a_{3}$, $a_{7}$ are the first three terms of a geometric sequence $\{b_{n}\}$.
(I) Find the general term formulas for both sequences $\{a_{n}\}$ and $\{b_{n}\}$;
(II) Let $c_{n}=a_{n}-b_{n}$, find the sum of the first $n$ terms of the sequence $\{c_{n}\}$.

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