
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 cities \( A, B, C, D \) are located at the vertices of a square with a side length of 100 km. A railway network needs to be designed so that each city is connected to any of the other three cities (it is permissible to create junction stations at points other than \( A, B, C, D \)) and the total length of the lines is minimized. What is the optimal network design and what is its total length?

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