
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 various flavors. Flavors are considered the same if the ratio of red to green candies is the same proportionally, thus ratios that reduce to the same simplest form are equivalent (e.g., 2 red / 1 green is the same as 4 red / 2 green). Given that at least one candy is used to make a flavor, how many different flavors can be created?

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