
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 an integer \( n \geq 5 \). Find the smallest integer \( m \) such that there exist two sets of integers \( A \) and \( B \) satisfying the following conditions:
1. \( |A| = n \), \( |B| = m \), and \( A \subseteq B \).
2. For any two different elements \( x \) and \( y \) in set \( B \), \( x+y \in B \) if and only if \( x, y \in A \).

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