
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 a triangular pyramid $P-ABC$ with lateral edges $PA$, $PB$, $PC$ being mutually perpendicular, which of the following statements are correct? Write down the numbers of all correct statements.

① $PA \perp BC$, $PB \perp AC$, $PC \perp AB$;  
② The perpendicular dropped from vertex $P$ to form the height of the triangular pyramid lands on the orthocenter of $\triangle ABC$;  
③ $\triangle ABC$ can be an obtuse triangle;  
④ The lines connecting the midpoints of opposite edges intersect at one point.

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