
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 200-sided polygon \( A_{1} A_{2} \cdots A_{200} \), connect the diagonals \( A_{i} A_{i+9} \) for \( i=1, 2, \cdots, 200 \), where \( A_{i+200}=A_{i} \) for \( i=1,2, \cdots, 9 \). How many different intersection points are there inside the regular 200-sided polygon formed by these 200 diagonals?

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