
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
When choosing any 4 vertices on a cube, they can be the vertices of the following geometric shapes. List all correct conclusions by their numbers.

① Rectangle;

② Parallelogram that is not a rectangle;

③ Tetrahedron with three faces being isosceles right triangles and one 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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