
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]


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A set of nine distinct colored equilateral triangles is available (each triangle a different color), but only eight are used to construct a regular octahedron. How many distinguishable ways are there to construct the octahedron? 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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