
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
The set \( X \) has \( n>1 \) elements, and there is a relation \(\wedge\) that satisfies the following properties:
1. For any \( x \in X \), \( x \wedge x \) does not hold;
2. For any pair of different elements \( x, y \in X \), exactly one of \( x \wedge y \) or \( y \wedge x \) holds;
3. If \( x \wedge y \), then there exists \( z \in X \) such that \( x \wedge z \) and \( z \wedge y \).

What is the minimum number of elements in \( X \)?

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