
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 $z$ each belong to the set $\{0,1,2,3\}$. Determine how many right-angled triangles can be formed where all the vertices of the triangle are in $T$ and at least one angle is $90^\circ$.
A) 72
B) 144
C) 216
D) 288
E) 360

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