
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
In the arithmetic sequence $\{a_n\}$, $a_2+a_7=-23$, $a_3+a_8=-29$.  
(I) Find the general formula for the sequence $\{a_n\}$.  
(II) Suppose the sequence $\{a_n+b_n\}$ is a geometric sequence with the first term being $1$ and the common ratio being $c$, find the sum of the first $n$ terms of $\{b_n\}$, $S_n$.

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