
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 preparation for a game of Fish, Carl must deal 48 cards to 6 players. For each card that he deals, he runs through the entirety of the following process:
1. He gives a card to a random player.
2. A player \( \mathrm{Z} \) is randomly chosen from the set of players who have at least as many cards as every other player (i.e., \( \mathrm{Z} \) has the most cards or is tied for having the most cards).
3. A player \( \mathrm{D} \) is randomly chosen from the set of players other than \( \mathrm{Z} \) who have at most as many cards as every other player (i.e., \( \mathrm{D} \) has the fewest cards or is tied for having the fewest cards).
4. \( \mathrm{Z} \) gives one card to \( \mathrm{D} \).

He repeats steps 1-4 for each card dealt, including the last card. After all the cards have been dealt, what is the probability that each player has exactly 8 cards?

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