
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 square-shaped area with sides of $10 \text{ km}$ has a parallel road running along two of its sides. There are five observation stations within the area. The goal is to construct connecting paths, parallel to the sides of the square, so that each station can reach any of the roads by bicycle. Bicycling on the roads themselves is not allowed.

What is the minimum total length of these connecting paths, regardless of the positions of the observation stations?

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