
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 \( M \) be a set composed of a finite number of positive integers,
\[ 
M = \bigcup_{i=1}^{20} A_i = \bigcup_{i=1}^{20} B_i, \text{ where}
\]
\[ 
A_i \neq \varnothing, B_i \neq \varnothing \ (i=1,2, \cdots, 20)
\]
satisfying the following conditions:
1. For any \( 1 \leqslant i < j \leqslant 20 \),
\[ 
A_i \cap A_j = \varnothing, \ B_i \cap B_j = \varnothing;
\]
2. For any \( 1 \leqslant i \leqslant 20, \ 1 \leqslant j \leqslant 20 \), if \( A_i \cap B_j = \varnothing \), then \( \left|A_i \cup B_j\right| \geqslant 18 \).

Find the minimum number of elements in the set \( M \) (denoted as \( |X| \) representing the number of elements in set \( X \)).

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