
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 an arithmetic sequence $\{a_n\}$ satisfying $a_1=3$ and $a_5=15$, and another sequence $\{b_n\}$ satisfying $b_1=4$ and $b_5=31$, suppose there is a geometric sequence $\{c_n\}$ satisfying $c_n=b_n-a_n$.  
(1) Find the general formula for sequences $\{a_n\}$ and $\{c_n\}$.  
(2) Find the sum of the first $n$ terms of sequence $\{b_n\}$.

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