
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 both of the smaller ones, and all three gears combined have 60 teeth. When the largest gear lacks 20 teeth to complete four full rotations, the second and third gears make 5 and 10 full rotations, respectively. How many teeth does each gear have individually?

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