
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 the plane;

b) in space

can they be arranged so that none of the angles \( M_i M_j M_k \) (where \( i, j, k \) are any of the numbers \( 1, 2, \ldots, n \)) will be obtuse?

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