
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
A magician has a set of $20^{2}$ different cards. Each card has one red side and one blue side; on each card, there is a natural number from 1 to 20 written on both sides. We call a card a double if the numbers on both sides of the card are the same. The magician wants to draw two cards in such a way that at least one of them is a double, and no number appears simultaneously on both drawn cards. In how many ways can he do this?

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