
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
The side length of a cube is 2, and it has 20 points which include all vertices and midpoints of each edge. By choosing any three of these points to form the vertices of a triangle, how many of such triangles have an area equal to $\frac{3}{2}$?

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