
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 $f(x)=\frac{m-{3}^{x}}{1+{3}^{x}}$ is an odd function.<br/>$(1)$ Find the value of the real number $m$;<br/>$(2)$ If the inequality $f(t^{2}+2t+k)+f(-2t^{2}+2t-5) \gt 0$ holds for any $t\in \left[0,5\right]$, find the range of the real number $k$.

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