
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 seven-pointed star in the sand, and at each of the 7 outward-pointing points and 7 inward-pointing points, he places one of fourteen 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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