
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 needs to build a warehouse. According to market research analysis, shipping costs are directly proportional to the distance between the factory and the warehouse, while storage costs are inversely proportional to this distance. When the distance between the factory and the warehouse is 4 kilometers, the shipping cost is 200,000 yuan, and the storage cost is 50,000 yuan. At what distance, in kilometers, will the sum of the shipping and storage costs be at its minimum, and what is the minimum cost in 10,000 yuan?

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