
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 $f(x)={e^x}-\frac{m}{{{e^x}}}$ defined on $R$ is an odd function (where $e$ is the base of natural logarithm).  
$(1)$ Find the value of the real number $m$;  
$(2)$ If $f\left(a-1\right)+f(2a^{2})\leqslant 0$, find the range of the real number $a$.

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