
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 decides to make the challenge a bit more complex by drawing a regular six-pointed star (a hexagram) in the sand, placing different unique objects at each point where lines intersect. Each point of the six outward-pointing tips and each point where two lines intersect internally (a total of twelve points) has a unique stone from John's collection of twelve stones. How many distinct ways can he place the stones given that arrangements considered as equivalent include rotations and reflections of the hexagram?

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