
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 $f(x)=a- \frac {1}{1+2^{x}}(a\in\mathbb{R})$,  
$(1)$ If $f(1)+f(-1)=0$, find the value of the real number $a$;  
$(2)$ Determine whether there exists a real number $a$ such that the function $f(x)$ is an odd function, and explain the reason.

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