
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
Four friends: Alice, Bob, Cindy, and Dave, play a modified version of the game. Each starts with $2. A bell rings every 15 seconds, at which time each of the players who currently have money simultaneously chooses one of the other three players independently and at random and gives $1 to that player. What is the probability that after the bell has rung 5 times, each player will have $2?
A) $\frac{1}{81^5}$
B) $\frac{4}{81^5}$
C) $\frac{10}{81^5}$
D) $\frac{20}{81^5}$

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