
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 $(x,y,z)$ where $x$, $y$, and $z$ are each chosen from the set $\{0,1,2,3\}$. Determine how many equilateral triangles have their vertices in $T$.
A) 150
B) 160
C) 170
D) 180
E) 190

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