
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 that $\{a_n\}$ is an arithmetic sequence satisfying $a_2=6$ and $a_5=15$, and that $\{b_n\}$ satisfies $b_2=8$ and $b_5=31$, also the sequence $\{b_n - a_n\}$ forms a geometric sequence.  
(1) Find the general formulas for the sequences $\{a_n\}$ and $\{b_n\}$.  
(2) Find the sum of the first $n$ terms of the sequence $\{b_n\}$.

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