
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 that $a$, $b$, and $c$ are real numbers, then:  
(1) "$a > b$" is a sufficient condition for "$a^2 > b^2$";  
(2) "$a > b$" is a necessary condition for "$a^2 > b^2$";  
(3) "$a > b$" is a sufficient condition for "$ac^2 > bc^2$";  
(4) "$a > b$" is a necessary and sufficient condition for "$|a| > |b|$". Among these, the false statements are.

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