
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
Rani, James, and Fiona start a game with $$3$ each. A bell rings every $10$ seconds, and at each ring, each of the players who has more than $1 dollar will give $$1$ to one of the other two players chosen at random. What is the probability that after the bell has rung $2025$ times, each player will have exactly $$3$?
A) $\frac{1}{27}$
B) $\frac{2}{27}$
C) $\frac{5}{27}$
D) $\frac{2}{9}$
E) $\frac{1}{9}$

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