
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
Five red candies and four green candies can be combined to make many different flavors. Flavors are defined by different percentages of red candies, so ratios with the same proportion are considered as the same flavor (e.g., 5 red / 1 green is the same flavor as 10 red / 2 green). If a flavor is to be made using some or all of the nine candies, how many different flavors are possible?

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