
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
Given 5 points, any 4 of which do not lie in the same plane.

a) How many tetrahedrons can be formed whose vertices are 4 of these points?
b) How many planes can be formed passing through triples of these points?
c) How many lines are determined by pairs of these points?

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