
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 with the sum of the first $n$ terms denoted as ${ S_n } \left( n \in \mathbb{N}^* \right)$, and ${ b_n }$ is a geometric sequence with the first term being 2 and a common ratio greater than 0. It is known that ${ b_2 + b_3 = 12 }$, ${ b_3 = a_4 - 2a_1 }$, 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 ${ a_{2n} b_{2n-1} } \left( n \in \mathbb{N}^* \right)$.

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