
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
A chimney is causing environmental pollution by spreading dust around the area. It is known that there are two chimneys, A and B, 3 km apart. The amount of dust emitted from chimney A is eight times that from chimney B. Environmental tests have shown that the concentration of dust on the ground at a point is inversely proportional to the square of the distance from the point to the chimney, and directly proportional to the amount of dust emitted from the chimney (with the proportionality constant k). Let C be a point on the line segment AB connecting the two chimneys (not including the endpoints), let AC be x km, and let the dust concentration at point C be y.
(Ⅰ) Write down the expression for y as a function of x;
(Ⅱ) Is there a point C where the dust concentration is minimal? If there is, find the distance of AC; if not, explain why.

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