
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
Two meshing gears \(A\) and \(B\) are mounted tightly: the first on shaft \(O_{1}\), and the second on shaft \(O_{2}\). Gear \(A\) has 10 more teeth than gear \(B\). At a certain rotational speed of shaft \(O_{1}\), shaft \(O_{2}\) makes 63 revolutions per minute. If the gears are swapped, then at the same speed of shaft \(O_{1}\), shaft \(O_{2}\) makes 28 revolutions. Determine the number of teeth on each gear.

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