
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 a cube, if we select 4 points and connect them to form a tetrahedron, then this tetrahedron could be: ① each face is a right-angled triangle, ② each face is an equilateral triangle, ③ there is exactly one face that is a right-angled triangle, ④ there is exactly one face that is an equilateral triangle. Among these statements, the correct ones are: (Write down the numbers of all correct statements)

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