
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 modified version of the game, Raashan, Sylvia, and Ted each start with different amounts of money: Raashan with $3, Sylvia with $1, and Ted with $1. A bell rings every 12 seconds, and each player with money chooses one of the other two players to give $1 to. However, if a player was chosen by both other players in the previous round, they have the option to keep their money for that round. What is the probability that after the bell has rung $2023$ times, each player will have exactly $2?
A) $\frac{1}{8}$
B) $\frac{1}{6}$
C) $\frac{1}{4}$
D) $\frac{1}{3}$
E) $\frac{1}{2}$

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