
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
Fold a square \( ABCD \) along the diagonal \( BD \) to form a dihedral angle \( A-BD-C \). Among the following four conclusions:  
① \( AC \) is perpendicular to \( BD \);  
② Triangle \( ACD \) is an equilateral triangle;  
③ The angle between \( AB \) and plane \( BCD \) is 60°;  
④ The angle formed by \( AB \) and \( CD \) is 60°.  
The correct conclusion(s) can be indicated by their number(s) ______.

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