
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
If the domain of the function $f(x)=\frac{b-2^{x}}{a+2^{x}}$ is $\mathbb{R}$ and it is an odd function.  
$(1)$ Find the values of $a$ and $b$;  

$(2)$ If for any $t \in \mathbb{R}$, the inequality $f(t^{2}-2t) < f(-2t^{2}+k)$ always holds, find the range of $k$.

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