
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
Mark creates a regular six-pointed star (hexagram), placing a unique colorful stone at each of the 12 points where lines intersect. If arrangements that are identical under rotations and reflections of the star are considered the same, how many distinct ways can Mark place the stones?

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