
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
Thirty-six players are playing a game: from a deck of 36 playing cards, the players take turns randomly drawing one card each. If a player draws the ace of diamonds, that player wins; if a different card is drawn, the player returns the card to the deck, and the next player takes a turn. The drawing continues in a loop: first player, then the second, and so on. If no one draws the ace of diamonds in the first round, the players continue to draw cards in the same order in the next round. This repeats until someone draws the ace of diamonds.

a) Is this a fair game, i.e., do all players have equal chances of winning?

b) Find an approximate probability of the first player winning.

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