
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 city of Cordisburgo, a bicycle race was held on a circular track, with three cyclists participating: Guimarães, Rosa, and João. In the first hour of the race, Guimarães completed exactly 230 full laps, João completed exactly 111 full laps, but it is unknown how many laps Rosa completed. It is known that Rosa completed an integer number of laps, more than João but fewer than Guimarães. Additionally, each cyclist rode at a constant speed, and they all started from the same point. Considering the overtakes made in the initial time, how many total overtakes were made in the first hour of the race?

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