
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
Given a bag containing one red, one yellow, and one blue ball, a ball is drawn from the bag with equal probability and replaced after noting its color. This process continues until two consecutive red balls are drawn. Let $X$ be the number of draws needed to achieve this. Find the expected value $\mathrm{E}(X)$ of $X$.

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