
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
Given seven red candies and five green candies, how many different flavors can be created? Flavors are differentiated based on the percentage of red candies, so ratios like $1$ red / $1$ green and $2$ red / $2$ green are considered the same flavor. A valid flavor must contain at least one candy.

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