
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
Given the following propositions:
① Through a point in space, it is always possible to draw a line that is perpendicular to two skew lines;
② Through a point in space, it is always possible to draw a plane that is parallel to two skew lines;
③ Given planes $\alpha$ and $\beta$, and lines $a$ and $b$, if $\alpha \cap \beta = a$, and $b \perp a$, then $b \perp \alpha$;
④ A prism with four lateral faces that are pairwise congruent is a right prism;
⑤ A pyramid with an equilateral triangle as its base and isosceles triangles as its lateral faces is a regular tetrahedron;
Among these propositions, the correct ones are numbered as follows.

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