
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 6 points in space such that no 4 points are coplanar, find the smallest positive integer $n$ such that whenever 10 line segments are drawn connecting these points, it is always possible to find $n$ distinct pairs of triangles, each pair sharing a common edge.

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