
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
Let \( T \) be the set of all points with coordinates \( (x, y, z) \), where \( x, y, \) and \( z \) are each chosen from the set \( \{0, 1, 2, 3\} \). How many equilateral triangles all have their vertices in \( T \)?
A) 92
B) 108
C) 120
D) 132
E) 144

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