
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
Abby, Bernardo, Carl, and Debra play a revised version of their game in which each starts with six coins. The game consists of five rounds. In each round, four balls are placed in an urn—two green, one red, and one white. The players each draw a ball at random without replacement. Each of the players who gets a green ball gives one coin to whoever gets the red ball. What is the probability that, at the end of the fifth round, each of the players has exactly six coins?
A) $\frac{1}{96}$
B) $\frac{1}{216}$
C) $\frac{1}{243}$
D) $\frac{1}{625}$

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