
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 isosceles right-angled triangles made of colored paper. Each triangle is a solid color with the same color on both sides of the paper. A large square is constructed from four of these paper triangles as shown. Two large squares 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 five different colors of triangles from which to choose, and the center triangle must be a different color from the corner triangles, how many distinguishable large squares can be constructed?

[asy]
draw((0,0)--(0,10)--(10,10)--(10,0)--cycle);
draw((0,0)--(5,5)--(0,10)--cycle);
draw((0,10)--(5,5)--(10,10)--cycle);
draw((10,0)--(5,5)--(10,10)--cycle);
draw((0,0)--(5,5)--(10,0)--cycle);
[/asy]

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