
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 a geometric sequence $\{a_n\}$ with a common ratio $q > 1$, the sum of the first $n$ terms is $S_n$, and $S_3 = 7$. Also, $a_1, a_2, a_3 - 1$ form an arithmetic sequence. For the sequence $\{b_n\}$, the sum of the first $n$ terms is $T_n$, and $6T_n = (3n+1)b_n + 2$, where $n \in \mathbb{N}^+$.  
(Ⅰ) Find the general formula for the sequence $\{a_n\}$.  
(Ⅱ) Find the general formula for the sequence $\{b_n\}$.  
(Ⅲ) Let set $A = \{a_1, a_2, \ldots, a_{10}\}$, $B = \{b_1, b_2, \ldots, b_{40}\}$, and $C = A \cup B$. Calculate the sum of all elements in set $C$.

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