
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 that the quality index $\xi$ (unit: millimeters) of a batch of components follows a normal distribution $N(25.40, \sigma^2)$, and $P(\xi \geq 25.45) = 0.1$. Now, randomly select $3$ components from this batch. Let $X$ represent the number of components out of these $3$ whose quality index value $\xi$ does not fall within the interval $(25.35, 25.45)$. Find $D(X)=$____.

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