
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 hexagonal shape in the sand, placing a different sea shell at each of its 6 corners and at the midpoint of each of the 6 sides, making 12 distinct points in total. In how many ways can he place 12 different sea shells, if only rotations of the arrangement are considered equivalent (reflections are not considered)?

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