
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 blue candies and four yellow candies are available to create various flavors. A flavor is defined by the percentage of blue candies used, so for instance, a combination of 5 blue / 0 yellow is the same flavor as 3 blue / 0 yellow; similarly, 4 blue / 2 yellow is the same as 2 blue / 1 yellow. 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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