
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
Suppose there is an arithmetic sequence $\{a_n\}$ with a common difference $d$ ($d \neq 0$) and a geometric sequence $\{b_n\}$ with a common ratio $q$ ($q > 0$). They meet the following conditions: $a_1 = b_1 = 2$, $a_7 = b_3$, and $a_{b_3} = 9$.
(Ⅰ) Find the general term formulas for $\{a_n\}$ and $\{b_n\}$.
(Ⅱ) Let $A = \{a_1, a_2, a_3, \ldots, a_{20}\}$ and $B = \{b_1, b_2, b_3, \ldots, b_{20}\}$, with $C = A \cap B$. Calculate the sum of the elements in set $C$.

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