
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 exponential function $y=g(x)$ satisfies: $g(3)=8$, and the function $f(x)= \dfrac {n-g(x)}{m+2g(x)}$ defined on domain $R$ is an odd function.  
$(1)$ Determine the expressions for $y=g(x)$ and $y=f(x)$;  
$(2)$ If $h(x)=f(x)+a$ has a zero point in $(-1,1)$, find the range of $a$;  
$(3)$ If for any $t∈(-4,4)$, the inequality $f(6t-3)+f(t^{2}-k) < 0$ always holds, find the range of the real number $k$.

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