
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
A crafts project involves constructing large equilateral triangles from four smaller congruent equilateral triangles of colored paper. Each small triangle is uniformly colored with the same color on both sides of the paper. A large equilateral triangle is defined as distinguishable if it cannot be superimposed onto another through translations, rotations, and reflections such that their constituent small triangles align in color. If there are eight different colors available for the triangles, how many distinguishable large equilateral triangles can be constructed?

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