
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 a geometric sequence $\{a_n\}$ with a common ratio $q > 1$, and $a_3+a_4+a_5=28$, $a_4+2$ is the arithmetic mean of $a_3$ and $a_5$. The sequence $\{b_n\}$ satisfies $b_1=1$, and the sum of the first $n$ terms of the sequence $\{(b_{n+1}-b_n)a_n\}$ is $2n^2+n$.
- (I) Find the value of $q$;
- (II) Find the general formula for the sequence $\{b_n\}$.

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