
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
You have five red candies and four green candies. These candies can be combined to create various flavors, where a flavor is defined by the percent of red candies present. Flavors are considered equivalent if their ratio of red to green is the same (e.g., 2 red / 1 green is the same as 4 red / 2 green). Determine how many distinct flavors can be made using some or all of these nine candies.

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