
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
Given the convex pentagon $ABCDE$, where each pair of neighboring vertices must have different colors and vertices at the ends of each diagonal must not share the same color, determine the number of possible colorings using 5 available colors.

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