
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
In a bag, there is one red, one yellow, and one blue ball. A ball is drawn from the bag each time (with equal probability for each color), its color is recorded, and then the ball is placed back in the bag. The process continues until two consecutive red balls are drawn. Let $\xi$ denote the number of draws made until this condition is met. Find the expected value of $\xi$.

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