
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 that $y=f\left(x\right)$ is an odd function defined on $R$, when $x\leqslant 0$, $f\left(x\right)=x^{2}+2x$.  
$(1)$ Find the analytical expression of the function $f\left(x\right)$ on $R$.  
$(2)$ If the function $f\left(x\right)$ is monotonically increasing on the interval $\left[-1,m-1\right]$, find the range of real number $m$.

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