
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 nearby. George performs the following operation five times: he draws a ball from the urn at random and then takes a ball of the same color from the box and returns both balls to the urn. After these five iterations, the urn contains eight balls. What is the probability that the urn contains three red balls and five blue balls?
- **A)** \( \frac{1}{21} \)
- **B)** \( \frac{2}{21} \)
- **C)** \( \frac{1}{7} \)
- **D)** \( \frac{1}{5} \)

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