
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
We have two gears. When they are connected, the ratio of the drive gear to the driven gear (the gear ratio) is $7:9$ or $9:7$. If we replace one gear with a gear having 3 fewer teeth and the other with a gear having 3 more teeth, the new ratio becomes $1:3$ or $3:1$. Which gear was replaced with one having fewer teeth? How many teeth do the four gears each have?

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