
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
Five red candies, four green candies, and two blue candies are available to make different flavored combos. A flavor is identified by the relative proportions of each colored candy, and those with the same proportion are the same flavor. How many distinct flavors can be created using some or all of these eleven candies?

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