
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
A gear mechanism has a smaller gear with 12 teeth and a larger gear with 32 teeth. Due to a manufacturing defect, one tooth on the smaller gear and one slot on the larger gear stick and make noise upon contact. At what intervals do we hear the squeaks if the larger gear takes 3 seconds for one full revolution? How can the squeaking be eliminated, assuming all other tooth-slot pairings are flawless and silent?

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