
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. Combinations forming unique flavors are distinguished only if the simplified ratio of red to green candies is unique (ignoring combinations without candies entirely). How many different flavors can be achieved using some or all of these nine candies?

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