
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 the sets \( A_{1}, A_{2}, \cdots, A_{n} \) are different subsets of the set \( \{1, 2, \cdots, n\} \), satisfying the following conditions:
(i) \( i \notin A_{i} \) and \( \operatorname{Card}(A_{i}) \geqslant 3 \) for \( i = 1, 2, \cdots, n \);
(ii) \( i \in A_{j} \) if and only if \( j \notin A_{i} \) for \( i \neq j \) and \( i, j = 1, 2, \cdots, n \).

Answer the following questions:
1. Find \( \sum_{i=1}^{n} \operatorname{Card}(A_{i}) \).
2. Find the minimum value of \( n \).

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