
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 game involving three friends—Rita, Sam, and Tom—each starts with different amounts of money. Rita starts with $2$, Sam starts with $1$, and Tom starts with $1$. A bell rings every $20$ seconds, at which time each of the players who currently have money independently and randomly selects one of the other two players and gives $1$ to that player. What is the probability that after the bell has rung $2020$ times, each player will have $1$?
A) $\frac{1}{4}$
B) $\frac{1}{8}$
C) $\frac{1}{16}$
D) $\frac{1}{32}$
E) $\frac{1}{64}$

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