
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 increasing arithmetic sequence, with $a_2 + a_5 = 17$ and $a_3 \cdot a_4 = 70$, and $\{b_n\}$ satisfies $2b_{n+1} = a_2b_n (n \in \mathbb{N}^*)$, and the sum of the first 5 terms is 62.

(Ⅰ) Find the general formula for $\{a_n\}$ and $\{b_n\}$;

(Ⅱ) Find the sum of the first $n$ terms of the sequence $\{a_{2n}b_{2n-1}\} (n \in \mathbb{N}^*)$.

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