
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 orange candies and four purple candies are available to create different flavors. A flavor is considered different if the percentage of orange candies is different. Combine some or all of these ten candies to determine how many unique flavors can be created based on their ratios.

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