
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 equation about $x$ is $x^{2}+2mx+m^{2}-1=0$.  
$(1)$ Without solving the equation, determine the situation of the roots of the equation and explain the reason.  
$(2)$ If $x_{1}$ and $x_{2}$ are two real roots of the equation, and $x_1(x_2+x_1)+x_2{}^2=5m$, find the value of $m$.

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