
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
At a distance of 20 km from a straight section of a railway track lies the village B. Where should the station C be located along the track such that the total travel time from A to B, traveling by train along AC and then by road along CB, is minimized? The speed of travel by train is 0.8 km per minute, and by road is 0.2 km per minute.

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