
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
In the 15th Jiangsu Grade 1 Trial, there is a straight street with 5 buildings numbered from left to right as 1, 2, 3, 4, 5. The building number _k_ has exactly _k_ (_k_ = 1, 2, 3, 4, 5) workers from Factory A, and the distance between two adjacent buildings is 50 meters. Factory A plans to build a station on this street. To minimize the total distance all workers from Factory A have to walk to the station, the station should be built at a distance of ______ meters from building 1.

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