
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
The monthly land occupation fee ($y_1$) is inversely proportional to the distance from the warehouse to the station, while the monthly inventory cost ($y_2$) is directly proportional to the distance to the station. The warehouse is built 10 kilometers away from the station, and these expenses are $y_1 = 20,000$ yuan and $y_2 = 80,000$ yuan, respectively. Determine the distance from the station at which the warehouse should be built to minimize the sum of these two costs.

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