
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 large equilateral triangle is constructed by arranging smaller equilateral triangles made of paper, each colored on both sides with the same color. There are eight different colors available. The large triangle is formed by placing one small triangle in the center and three others at the corners within the outline of the large triangle, as described:

[asy]
draw((0,0)--(10,0)--(5,8.7)--cycle);
draw((5,0)--(2.5,4.3)--(7.5,4.3)--cycle);
[/asy]

Two large triangles are considered distinguishable if it is not possible to place one on the other such that all corresponding small triangles match in color, even using translations, rotations, and reflections. How many distinguishable large equilateral triangles can be formed?

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