
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 certain distributor plans to purchase a batch of products and rent a warehouse for storage. After research, the monthly rent cost $y_{1}$ (unit: ten thousand yuan) is inversely proportional to the distance $x$ (unit: km) from the storage warehouse to the store, and the monthly cost of transporting from the storage warehouse to the store $y_{2}$ (unit: ten thousand yuan) is directly proportional to $x$. If the storage warehouse is rented at a distance of $5$ km from the store, then $y_{1}$ and $y_{2}$ are $1$ ten thousand yuan and $4$ ten thousand yuan, respectively. To reduce costs, the distributor should rent the storage warehouse at a distance of ______ km from the store in order to minimize the sum of the two costs.

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