
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
2005 children, numbered 1 to 2005, participate in a game. 2005 cards, numbered 2 to 2006, are prepared. Each child is to be distributed one card. It is required that the number on the card given to each child must be a multiple of the number of the child. In how many different ways can the cards be distributed?

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