
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 a plane with a certain number of points, none of which lie on a straight line connecting any two other points. Each point is marked with either red, white, or green color. The number of lines connecting pairs of points with different colors is 213, and the number of lines connecting pairs of points with the same color is 112. Among the triangles determined by these points, the number of triangles with vertices all marked in different colors is 540. The number of triangles with exactly two red vertices is 612. What can be said about the number of triangles with exactly two white vertices?

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