
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
Let \( A=\{1,2,3,4,5,6\} \) and \( B=\{7,8,9, \cdots, n\} \). Choose 3 numbers from \( A \) and 2 numbers from \( B \) to form a set of 5 elements, denoted as \( A_{i} \) (\( i=1,2,3, \cdots, 20 \)), such that \(\left|A_{i} \cap A_{j}\right| \leqslant 2 \) for \( 1 \leqslant i < j \leqslant 20 \). Find the minimum value of \( n \).

(2002 IMO China National Team Selection Test)

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