
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 that \( P_{1}, P_{2}, \cdots, P_{100} \) are 100 points on a plane, with no three points being collinear. For any three of these points, if their indices, when arranged in increasing order, form a clockwise direction, then the triangle formed by these three points is called a "clockwise triangle." Is it possible for there to be exactly 2017 clockwise triangles?

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