
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 \(\{0,1\}\). Determine the number of equilateral triangles where all vertices are in \( T \).
- **A)** 6
- **B)** 8
- **C)** 10
- **D)** 12
- **E)** 14

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