
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
Eight red candies and five green candies are available to create various candy flavors. A flavor is considered unique based on the percentage of red candies present, hence, 4 red / 0 green would taste the same as 8 red / 0 green; similarly, 6 red / 3 green is the same as 2 red / 1 green. Determine the number of different flavors possible using some or all of the thirteen candies.

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