
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 supply of extra red and blue balls is available nearby. George performs the following operation five times: he draws a ball from the urn at random and then adds two balls of the same color from the supply before returning all balls to the urn. After the five operations, the urn contains thirteen balls. What is the probability that the urn contains nine red balls and four blue balls?
**A) $\frac{1920}{10395}$**
**B) $\frac{1024}{10395}**
**C) $\frac{192}{10395}**
**D) $\frac{960}{10395}**

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