
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 congruent equilateral triangles made of colored paper. Each triangle is a solid color with the same color on both sides of the paper. A large equilateral triangle is constructed from five of these paper triangles as shown. Three triangles form the outer corners, one triangle forms the center, and another triangle is placed between the center and one of the corners. Two large triangles are considered distinguishable if one cannot be transformed into the other through translations, rotations, and/or reflections such that their corresponding small triangles match in color. If there are eight different colors of triangles available, how many distinguishable large equilateral triangles can be created?

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