
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
An urn initially contains two red and two blue balls. If John performs four rounds of a modified operation, where at each round he removes one ball from the urn at random, then draws one of the remaining balls at random and adds one of the same color, calculate the probability that the urn contains three balls of each color after the four operations.

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