
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
Three friends, Rowan, Sara, and Tim, are playing a monetary game. Each starts with $3. A bell rings every 20 seconds, and with each ring, any player with money chooses one of the other two players independently at random and gives them $1. The game continues for 2020 rounds. What is the probability that at the end of the game, each player has $3?
A) $\frac{1}{8}$
B) $\frac{1}{4}$
C) $\frac{1}{3}$
D) $\frac{1}{2}$

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