
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
A set  $ E$  of points in the 3D space let  $ L(E)$  denote the set of all those points which lie on lines composed of two distinct points of  $ E.$   Let  $ T$  denote the set of all vertices of a regular tetrahedron. Which points are in the set  $ L(L(T))?$ 

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