
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
Find the smallest \( n \) such that there is a directed graph on \( n \) points satisfying the following conditions:
1. There is at most one edge between any pair of points.
2. If there is an edge from \( A \) to \( B \), then there is a point \( C \) such that there are edges from \( A \) to \( C \) and from \( C \) to \( B \).
3. Given any point \( A \), there is a point \( B \) such that there is an edge from \( A \) to \( B \).

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