
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
In a deck of  $N$  cards, the cards are denoted by  $1$  to  $N$ . These cards are dealt to  $N$  people twice. A person  $X$  wins a prize if there is no person  $Y$  who got a card with a smaller number than  $X$  both times. Determine the expected number of prize winners.

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