
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 $f\left(x\right)=\frac{m•{2}^{x}-1}{{2}^{x}+1}$ is an odd function defined on $R$.  
$(1)$ Find the value of the real number $m$;  
$(2)$ If the inequality $f\left(x-3\right)+f(a+x^{2}) \gt 0$ always holds, find the range of the real number $a$.

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