
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
Among the following propositions, the correct ones are numbered as:

① Through any point in space, there can be exactly one plane parallel to two given skew lines;  
② Given a plane $\alpha$, and two lines $a$ and $b$, with $a \cap \alpha = a$, $b \perp a$, then $b \perp \alpha$;  
③ A prism with two lateral faces perpendicular to the base is a right prism;  
④ In a tetrahedron, if two pairs of opposite edges are perpendicular to each other, then the third pair of opposite edges must also be perpendicular;  
⑤ The four faces of a tetrahedron can all be right triangles.

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