
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 certain mechanism, three gears of different diameters are interconnected in such a way that the largest gear touches the two smaller ones. Combined, the three gears have a total of 60 teeth. When the largest gear falls short by 20 teeth of making a full four revolutions, the second and third gears make 5 and 10 complete revolutions, respectively. How many teeth does each gear individually have?

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