
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
If a point's ordinate is twice its abscissa, then this point is called a double point. If there exist two double points $M(x_{1}, y_{1})$ and $N(x_{2}, y_{2})$ on the graph of the quadratic function $y=x^{2}+2mx-m$ (where $m$ is a constant), and $x_{1} < 1 < x_{2}$, find the range of values for $m$.

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