
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 there are 5 points in the plane no three of which are collinear, draw all the segments whose vertices are these points, and determine the minimum number of new points made by the intersection of the drawn segments.

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