
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 the function $f(x)=ax- \frac {b}{x}-2\ln x$, for any real number $x > 0$, it holds that $f(x)=-f( \frac {1}{x})$.  
$(1)$ Find the sum of all zeros of the function $y=f(e^{x})$;  
$(2)$ For any real number $x\geqslant 1$, the function $f(x)\geqslant 0$ always holds, find the range of the real number $a$.

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