
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 $f(x)= \frac {2^{x}-a}{2^{x}+a}$ ($a > 0$) is an odd function on its domain.  
$(1)$ Find the value of $a$;  
$(2)$ Determine the monotonicity of the function $f(x)$ and provide a proof;  
$(3)$ Find the maximum value of $f(x)$ on $(-\infty,1]$.

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