
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 5000 cards, each containing a unique natural number from 1 to 5000 (each number appears exactly once). You need to select two cards such that the sum of the numbers on them is divisible by 100. In how many ways can this be done?

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