
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
In a plane, there are 18 points, no three of which are collinear. Each pair of points is connected by a line segment, and each line segment is colored either red or blue. Any one point $A$ has an odd number of red line segments emanating from it, and for the remaining 17 points, the number of red line segments emanating from them are all different. Determine the number of triangles, each of which has its vertices among the given points, that either have all sides red or have two sides red and one side blue.

(Note: This problem appeared in the 1994 Hunan Province Training Team Test.)

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