
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 a geometric sequence satisfying $a_2=6$ and $a_3=-18$, and the sequence $\{b_n\}$ satisfies $b_1=2$, and $\{2b_n+a_n\}$ is an arithmetic sequence with a common difference of $2$.  
(Ⅰ) Find the general formula for sequences $\{a_n\}$ and $\{b_n\}$.  
(Ⅱ) 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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