
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, $\{b_n\}$ is a monotonically increasing geometric sequence, and $a_2=b_2=3$, $b_1+b_3=10$, $b_1b_3=a_5$.  
(I) Find the general formula for the sequence $\{a_n\}$.  
(II) Let $c_n=\begin{cases}a_n & (n\leqslant 5) \\  b_n & (n > 5)\end{cases}$, determine 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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