
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, the sum of the first $n$ terms is denoted as $S_n (n \in N^{+})$, and $\{b_n\}$ is a geometric sequence with the first term being 2 and a common ratio greater than 0. It is known that $b_2 + b_3 = 12$, $b_3 = a_4 - 2a_3$, and $S_{11}=11b_4$.

1. Find the general term formulas for both sequences $\{a_n\}$ and $\{b_n\}$.
2. Find the sum of the first $n$ terms of the sequence $\{a_{2n}b_{2n-1}\} (n\in N^{+})$.

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