
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
If the base $BCD$ of a tetrahedron $A-BCD$ is an equilateral triangle, and the projection of vertex $A$ on the base $BCD$ is the center of $\triangle BCD$, then such a tetrahedron is called a regular tetrahedron. The following conclusions are given:  
① In a regular tetrahedron $A-BCD$, it must be that $AB \perp CD$, $BC \perp AD$, $AC \perp BD$;  
② In a regular tetrahedron $A-BCD$, the midpoints of all opposite edges must intersect at one point;  
③ When all the edges of a regular tetrahedron $A-BCD$ are of equal length, the ratio of the radii of the inscribed sphere to the circumscribed sphere is 1:2;  
④ If the lateral edges of a regular tetrahedron $A-BCD$ are all 2, and the apex angle of a lateral triangle is 40°, and a plane passing through point B intersects the lateral edges $AC$, $AD$ at $M$, $N$, respectively, then the minimum perimeter of $\triangle BMN$ is equal to $2 \sqrt {3}$.  
The correct conclusions are \_\_\_\_\_\_ . (Write down the numbers of all correct statements).

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