
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
Eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron. Two triangles that share an edge are fixed as red and blue, respectively. How many distinguishable ways are there to arrange the colors of the other six triangles, ensuring that the octahedron remains distinguishable under rotation? (Two colored octahedrons are distinguishable if neither can be rotated to look just like the other.)

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