
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
For what number \( n \) of points \( M_{1}, M_{2}, \ldots, M_{n} \)

a) in a plane;

b) in space

can they be arranged such that all triangles \( M_{i} M_{j} M_{k} \) (where \( i, j, k=1,2, \ldots, n \) ) are right-angled?

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