
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
Suppose you have 3 red candies, 2 green candies, and 4 blue candies. A flavor is defined by the ratio of red to green to blue candies, and different flavors are identified by distinct ratios (flavors are considered the same if they can be reduced to the same ratio). How many different flavors can be created if a flavor must include at least one candy of each color?

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