
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 balls and one blue ball. A box of extra red and blue balls is available. George performs five operations as follows: he draws a ball from the urn at random and then adds two balls of the same color from the box to the urn. After these five operations, determine the probability that the urn contains seven red balls and four blue balls.

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