
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
Four congruent equilateral triangles, each of a different color, are used to construct a regular tetrahedron. How many distinguishable ways are there to construct the tetrahedron? (Two colored tetrahedrons are distinguishable if neither can be rotated to look just like the other.)
[asy] import three; import math; unitsize(1.5cm); currentprojection=orthographic(2,0.2,1); triple A=(1,1,1); triple B=(-1,-1,1); triple C=(-1,1,-1); triple D=(1,-1,-1); draw(A--B--C--cycle); draw(A--C--D--cycle); draw(A--D--B--cycle); draw(B--C--D--cycle); [/asy]

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