
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
There is an unlimited supply of equilateral triangles made of colored paper, each triangle being a solid color with the same color on both sides. A large equilateral triangle is constructed from four of these triangles. The triangles are arranged in such a way that no two adjacent triangles (including those at the corners and edges) have the same color. Two large triangles are considered distinguishable if it is not possible to place one on the other, using translations, rotations, and/or reflections, so that their corresponding small triangles are of the same color. Given that there are eight different colors of triangles from which to choose, how many distinguishable large equilateral triangles can be constructed?

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