
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
John draws a regular six-pointed star (hexagram) in the sand. At each of the 12 points, he places one of twelve different sea shells. How many ways can he place the shells, if reflections and rotations of an arrangement are considered equivalent?

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