
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]


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A steel pipe production workshop produces a large batch of steel pipes. The quality inspector randomly selects several pipes to measure their diameters (in mm) and finds that the diameters (X) of these steel pipes follow a normal distribution N(65, 4.84). When the quality inspector randomly inspects, he measures a pipe with a diameter of 73mm and immediately requests to stop production for equipment inspection.
(I) Based on your knowledge, judge whether the decision of the quality inspector is reasonable, and explain the basis for your judgment.
(II) If 100 pipes are randomly selected from this batch of steel pipes, and the number of pipes with diameters between 60.6mm and 65mm is a random variable ξ, (i) find the mathematical expectation of the random variable ξ, and (ii) find the integer value k when P(ξ=k) reaches the maximum.

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