
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
Consider a set $T$ consisting of points $(x,y,z)$ where each of $x$, $y$, and $z$ is chosen from $\{0, 1, 3\}$. Determine how many equilateral triangles have all their vertices among points in $T$.
A) 48
B) 52
C) 56
D) 60
E) 64

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