
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
An automated machine produces rollers, monitoring their diameters $X$. Assuming that the random variable $X$ is normally distributed with parameters $a=10$ mm and $\sigma=0.1$ mm, find the interval within which the diameters of the rollers will fall with a probability of 0.9973.

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