
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 set \( M \) consisting of a finite number of positive integers, where \( M = \bigcup_{i=1}^{20} A_i = \bigcup_{i=1}^{20} B_i \). Here, each \( A_i \neq \emptyset \) and each \( B_i \neq \emptyset \) for \( i = 1, 2, \ldots, 20 \). Additionally, for any \( 1 \leq i < j \leq 20 \), it holds that \( A_i \cap A_j = \emptyset \) and \( B_i \cap B_j = \emptyset \). 

It is known that for any \( 1 \leq i \leq 20 \) and \( 1 \leq j \leq 20 \), if \( A_i \cap B_j = \emptyset \), then \( \left|A_i \cup B_j\right| \geq 18 \). Find the minimum number of elements in set \( M \).

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