
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
For the function $f(x)=a- \frac {2}{2^{x}+1}(a\in\mathbb{R})$

$(1)$ Determine the monotonicity of the function $f(x)$ and provide a proof;

$(2)$ If there exists a real number $a$ such that the function $f(x)$ is an odd function, find $a$;

$(3)$ For the $a$ found in $(2)$, if $f(x)\geqslant \frac {m}{2^{x}}$ holds true for all $x\in[2,3]$, find the maximum value of $m$.

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