
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
Six red candies and five green candies are available to create different flavors. Flavors are considered different only if the percentage of red compared to green differs, so ratios of red to green like 3:0 and 6:0 represent the same flavor. How many unique flavors can be formulated using some or all of these eleven candies?

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