
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
Alfred, Bruno, Christophe, and Damien are playing cards with a deck of 32 cards. Damien deals all the cards to the players. When it is pointed out that the number of cards among the players is different, Damien says, "If you want all of us to have an equal number of cards, do as I say. Alfred, divide half of your cards equally between Bruno and Christophe. Then let Bruno divide half of his cards equally between Christophe and Alfred, and let Christophe divide half of his cards equally between Alfred and Bruno."

How many cards did Damien initially deal to each player?

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