
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
**Text**: On a cube, select any 4 vertices. They could be the vertices of the following geometric shapes. Please list all the geometric shapes that match the description.

1. Rectangle
2. Parallelogram that is not a rectangle
3. Tetrahedron with three faces being isosceles right triangles and the other face being an equilateral triangle
4. Tetrahedron with each face being an equilateral triangle
5. Tetrahedron with each face being a right triangle

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