
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 game where each starts with five coins and there are five rounds. In each round, five balls are placed in an urn—two green, two red, and one blue. Each player draws a ball at random without replacement. If a player draws a green ball, they give one coin to a player who draws a red ball. If anyone draws a blue ball, no transaction occurs for them. What is the probability that at the end of the fifth round, each of the players has five coins?
**A)** $\frac{1}{120}$  
**B)** $\frac{64}{15625}$  
**C)** $\frac{32}{3125}$  
**D)** $\frac{1}{625}$  
**E)** $\frac{4}{125}$

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