
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
The popular variable-speed bicycle installs gears with different numbers of teeth on the driving and rear axles. By connecting different gear combinations with a chain, several different speeds can be achieved through different transmission ratios.

The "Hope" variable-speed bicycle has three gears on the driving axle with 48, 36, and 24 teeth, respectively, and four gears on the rear axle with 36, 24, 16, and 12 teeth, respectively. Question: How many different speeds does this variable-speed bicycle have in total?

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