
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
When $a>0$, $b>0$, the following inequalities are given:  
1. $(a+b)\left(\frac{1}{a}+\frac{1}{b}\right) \geq 4$;  
2. $a^2+b^2+2 \geq 2a+2b$;  
3. $\sqrt{|a-b|} \geq \sqrt{a} - \sqrt{b}$;  
4. $\frac{2ab}{a+b} \geq \sqrt{ab}$.  

Among these inequalities, the ones that always hold are __________. (Fill in the serial numbers)

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