
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 $f(x)=x^{2}+mx-1$, where $m\in\mathbb{R}$.  
$(1)$ If the solution set of the inequality $f(x) < 0$ with respect to $x$ is $\{x|-2 < x < n\}$, find the values of the real numbers $m$ and $n$;  
$(2)$ If for any $x\in[m,m+1]$, $f(x) < 0$ holds, find the range of values for the real number $m$.

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