
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 $\{a_n\}$ and an arithmetic sequence $\{b_n\}$, where $a_1 = b_1 = 1$ and $a_1 \neq a_2$, the terms $a_1$, $a_2$, $b_3$ form an arithmetic sequence, and the terms $b_1$, $a_2$, $b_4$ form a geometric sequence.  
(Ⅰ) Find the general formula for $\{a_n\}$ and $\{b_n\}$.  
(Ⅱ) Let $S_n$ and $T_n$ be the sum of the first $n$ terms of the sequences $\{a_n\}$ and $\{b_n\}$, respectively. If $S_n + T_n > 100$, find the minimum value of $n$.

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