
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
Call the Graph the set which composed of several vertices  $P_1,\ \cdots P_2$  and several edges  $($ segments $)$  connecting two points among these vertices. Now let  $G$  be a graph with 9 vertices and satisfies the following condition.

Condition: Even if we select any five points from the vertices in  $G,$  there exist at least two edges whose endpoints are included in the set of 5 points.

What is the minimum possible numbers of edges satisfying the condition?

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