
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 factory A is located 20km vertically away from a railway line, with the foot of the perpendicular being B. There is a raw material supply station C on the railway line 100km away from B. It is planned to build a material transfer station D somewhere between the railway BC, and then construct a road from station D to the factory. Given that the ratio of the freight cost per kilometer for the railway to that for the road is 3:5, where should D be located to minimize the freight cost from the supply station C to the factory?

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