
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 logistics company plans to establish a warehouse to store goods. After market research, the following information is obtained: the monthly land occupation fee $y_{1}$ (unit: ten thousand yuan) is inversely proportional to the distance $x$ (unit: km) from the warehouse to the station, and the monthly inventory fee $y_{2}$ (unit: ten thousand yuan) is directly proportional to $x$. If a warehouse is established at a distance of $10$ km from the station, then $y_{1}$ and $y_{2}$ are $4$ ten thousand yuan and $16$ ten thousand yuan, respectively. Find the value of $x$ when the sum of the two fees is minimized.

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