
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 in the sand, placing a unique sea shell at each of the 6 outward-pointing and 6 inward-pointing vertices, making a total of 12 different points with 12 different sea shells. How many ways can he arrange the shells if reflections and rotations of the arrangement are considered equivalent?

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