
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
On a spherical planet with an equator length of 1, it is planned to build \( N \) ring roads, each of which will follow a circumference of length 1. Then, several trains will be launched on each road. All trains will travel on the roads at the same positive constant speed, never stopping and never colliding. What is the maximum possible total length of all trains under these conditions? Consider trains as arcs of zero thickness, excluding the end points. Solve the problem for the cases: a) \( N = 3 \); b) \( N = 4 \).

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