
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
Among the following four numbers, the number of positive numbers is ______.  
① $\frac {b+m}{a+m} - \frac {b}{a}$, where $a>b>0$, $m>0$;  
② $(\sqrt {n+3} + \sqrt {n}) - (\sqrt {n+2} + \sqrt {n+1})$, where $n\in\mathbb{N}^*$;  
③ $2(a^2+b^2) - (a+b)^2$, where $a, b\in\mathbb{R}$;  
④ $\frac {x^{2}+3}{ \sqrt {x^{2}+2}} - 2$, where $x\in\mathbb{R}$.

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