
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 the function $f(x)=\frac{m-{3}^{x}}{n+{3}^{x}}$ with the domain of $R$ is an odd function.<br/>$(1)$ Find the values of $m$ and $n$;<br/>$(2)$ If there exists $t\in \left[0,4\right]$ such that $f(k-2t^{2})+f(4t-2t^{2}) \lt 0$ holds, find the range of values for $k$.

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