
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 that sets \( A \) and \( B \) are sets of positive integers with \( |A| = 20 \) and \( |B| = 16 \). The set \( A \) satisfies the following condition: if \( a, b, m, n \in A \) and \( a + b = m + n \), then \( \{a, b\} = \{m, n\} \). Define
\[ A + B = \{a + b \mid a \in A, b \in B\}. \]

Determine the minimum value of \( |A + B| \).

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