
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 $f(x)=\left\{\begin{array}{l}-{x^2}+ax,x≥0\\ m{x^2}+nx,x＜0\end{array}\right.$ defined on $R$ is an odd function.<br/>$(1)$ When $a=4$, find the values of $m$ and $n$;<br/>$(2)$ If the function $f\left(x\right)$ is monotonically decreasing on $\left[0,+\infty \right)$.<br/>$(i)$ Find the range of real numbers for $a$;<br/>$(ii)$ If the inequality $f\left(m-1\right)+f(m^{2}+t) \lt 0$ holds for any real number $m$, find the range of real numbers for $t$.

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