
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
Each vertex of a convex hexagon $ABCDEF$ is to be assigned a color. There are $8$ colors to choose from, and the ends of each diagonal, as well as adjacent vertices, must have different colors. How many different colorings are possible?
A) 15120
B) 17280
C) 20160
D) 23760

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