
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 ten-pointed star in the sand, each with 10 outward-pointing and 10 inward-pointing points. He places one of twenty different sea shells at each of these 20 points. How many ways can he place the shells, if reflections and rotations of the arrangement are considered equivalent?

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