
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
Suppose there is a bag containing one red, one yellow, and one blue ball. Each time a ball is drawn from the bag (the probability of drawing any particular color ball is the same), the color is noted, and then the ball is replaced into the bag. This process continues until two consecutive red balls are drawn. Let $\xi$ denote the number of draws at that point. What is the expected value of $\xi$?

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