
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 a quadratic equation in $x$: $2x^{2}+4x+m=0$.  
$(1)$ If $x=1$ is one of the roots of the equation, find the value of $m$ and the other root of the equation.  
$(2)$ If $x_{1}x_{2}$ are two real roots of the equation, and satisfy ${x}_{1}^{2}+{x}_{2}^{2}+5{x}_{1}{x}_{2}-{x}_{1}^{2}{x}_{2}^{2}=0$, find the value of $m$.

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