
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 are two red balls and one black ball in a bag. Except for the color, everything else is the same. Now, drawing with replacement is performed, where one ball is drawn at a time, its color is recorded, and then it is put back into the bag. This process is repeated three times consecutively. Let $X$ represent the number of times a red ball is drawn in these three attempts. Each ball has an equal probability of being drawn, and each draw is independent of the others. Determine the variance $D(X)$.

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