
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 $a$ is a real number, and the function $$f(x)=1- \frac {a}{2^{x}+1}.$$  
(1) If $f(-1)=-1$, find the value of $a$;  
(2) Determine whether there exists a real number $a$ such that $f(x)$ is an odd function;  
(3) If the function $f(x)$ has a zero in its domain, find the range of values for the real number $a$.

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