
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
The one-variable quadratic equation about $x$ is $x^{2}+2mx+m^{2}+m=0$ and it has two distinct real roots.<br/>$(1)$ Find the range of values for $m$.<br/>$(2)$ Let $x_{1}$ and $x_{2}$ be the two roots of the equation, and $x_{1}^{2}+x_{2}^{2}=12$. Find the value of $m$.

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