
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
Raashan, Sylvia, and Ted play a modified version of their previous game. Each starts with $1. This time, a bell rings every 10 seconds, and each of the players who have money can either choose to give $1 to one of the other two players at random or decide not to give money at all (holding their dollar). What is the probability that after the bell has rung 2024 times, each player will have $1?
A) $\frac{5}{27}$
B) $\frac{1}{4}$
C) $\frac{1}{3}$
D) $\frac{1}{2}$
E) $\frac{2}{3}$

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