
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 regular 2000-sided polygon \(A_1 A_2 \cdots A_{2000}\), consider the 2000 diagonals \(A_i A_{i+17}\) for \(i = 1, 2, \ldots, 2000\), where \(A_{i+2000} = A_i\) for \(i = 1, 2, \ldots, 17\). Find the number of distinct intersection points of these 2000 diagonals inside the regular 2000-sided polygon.

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