
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 2414 cards, each with a unique natural number from 1 to 2414. We need to choose 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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