
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
Consider an $8$-sided die where each face has a unique number from 1 to 8. How many ways can you paint two faces of the die red, such that the sum of the numbers on the red faces is not equal to 9, and one additional face blue, such that the blue face's number is not directly consecutive (in circular sequence) to either of the red-painted numbers?

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