
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
In a crown, five diamonds are embedded at five positions, equally spaced around a circle. If there are three different colors of diamonds to choose from, how many different ways are there to embed the diamonds? Assume that the five positions are indistinguishable from each other.

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