
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 statements:  
① If $ac > bc$, then $a > b$;  
② If $a < b$, then $ac^2 < bc^2$;  
③ If $\frac{1}{a} < \frac{1}{b} < 0$, then $a > b$;  
④ If $a > b$ and $c > d$, then $a - c > b - d$;  
⑤ If $a > b$ and $c > d$, then $ac > bd$.  
Among these statements, the correct ones are \_\_\_\_\_\_.

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