
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 $a > 0 > b > -a$, and $c < d < 0$, then among the following statements:  
(1) $ad > bc$; (2) $\frac{a}{b} + \frac{b}{c} < 0$; (3) $a - c > b - d$; (4) $a(d - c) > b(d - c)$  
The correct statements are __________.

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