
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 from a set of 7 colors, subject to the rules that no two adjacent vertices can share the same color, and no three consecutive vertices (such as ABC or DEF) can use colors that appear in a repeating sequence. Determine the number of different coloring configurations possible.

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