
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 $\{a_n\}$, $a_2 + a_7 = -23$, $a_3 + a_8 = -29$.  
(1) Find the general term formula of the sequence $\{a_n\}$.  
(2) Suppose the sequence $\{a_n + b_n\}$ is a geometric sequence with the first term 1 and common ratio 2, find the sum of the first $n$ terms of $\{b_n\}$, denoted $S_n$.

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