
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, where each triangle is a solid color. A large equilateral triangle is constructed from four of these paper triangles, and two large triangles are considered distinguishable if they cannot be matched by translations, rotations, and/or reflections. Given that there are 8 different colors of triangles to choose from, how many distinguishable large equilateral triangles can be constructed?

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