
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 an arithmetic sequence $\{a_n\}$ where the sum of the first $n$ terms is $S_n$, and it's known that $a_1 = 1$, and $S_3 = 9$. For the sequence $\{b_n\}$, we have $b_1 = 1$, and $b_3 = 20$.
(Ⅰ) If the sequence $\left\{\frac{b_n}{a_n}\right\}$ forms a geometric sequence with a common ratio $q > 0$, find $a_n$ and $b_n$.
(Ⅱ) Under the condition (I), find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$.

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