
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 there are two red balls and one black ball in a bag, with the only difference being color and all other aspects being identical, a ball is drawn each time, its color recorded, and then returned to the bag, this process is repeated three times. Let X represent the number of times a red ball is drawn. The probability of drawing each ball is the same, and each draw is independent. Find the variance D(X).

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