
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
Among five points $A, B, C, D, E$ in space, any four points are non-coplanar and the distances between any two points are distinct. For each tetrahedron formed by selecting four out of the five points, the shortest edge is colored black. After all the edges have been colored, the number of black segments emanating from a point is called the "wish number" of that point. What is the maximum value of the wish number among these points?

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