
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 a relay race from Moscow to Petushki, two teams of 20 people each participated. Each team divided the distance into 20 segments (not necessarily equal) and assigned them among the participants so that each person ran exactly one segment (each participant's speed is constant, but the speeds of different participants can vary). The first participants of both teams started simultaneously, and the baton handoff happens instantaneously. What is the maximum number of overtakes that could occur in such a race? An overtake at the segment boundaries is not counted.

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