
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. George undertakes the operation of randomly drawing a ball and then adding two more balls of the same color from a box into the urn. This operation is done three times. After these operations, the urn has a total of nine balls. What is the probability that there are exactly five red balls and four blue balls in the urn?
A) $\frac{1}{10}$
B) $\frac{2}{10}$
C) $\frac{3}{10}$
D) $\frac{4}{10}$
E) $\frac{5}{10}$

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