
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 there exist two different points $A(x_{1},y_{1})$ and $B(x_{2},y_{2})$ on the graph of the function $f(x)$, where $x_{1}$, $y_{1}$, $x_{2}$, $y_{2}$ make the maximum value of $|x_{1}x_{2}+y_{1}y_{2}|- \sqrt { x_{ 1 }^{ 2 }+ y_{ 1 }^{ 2 }}\cdot \sqrt { x_{ 2 }^{ 2 }+ y_{ 2 }^{ 2 }}$ equal to $0$, then the function $f(x)$ is called a "Cauchy function". Given the following functions:  
$①f(x)=\ln x(0 < x < 3)$;                 $②f(x)=x+ \dfrac {1}{x}(x > 0)$;  
$③f(x)= \sqrt {2x^{2}+8}$;                      $④f(x)= \sqrt {2x^{2}-8}$.  
Among these, the "Cauchy functions" are \_\_\_\_\_\_ (fill in all correct answer numbers).

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