
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
From the 8 vertices of the cube ABCD-A<sub>1</sub>B<sub>1</sub>C<sub>1</sub>D<sub>1</sub>, 4 different vertices are randomly selected. These 4 vertices could be the vertices of:
(1) A rectangle;
(2) A tetrahedron with each face being an equilateral triangle;
(3) A tetrahedron with each face being a right triangle;
(4) A tetrahedron with three faces being isosceles right triangles and one face being an equilateral triangle.  
Among these, the correct conclusions are \_\_\_\_\_\_\_\_.

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