
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
If $a$ and $b$ are rational numbers, then among the following statements:  
(1) If $|a| = b$, then $a = b$ must hold; (2) If $|a| > |b|$, then $a > b$ must hold; (3) If $|a| > b$, then $|a| > |b|$ must hold; (4) If $|a| = b$, then $a^2 = (-b)^2$ must hold. The correct one is (fill in the serial number).

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