
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 that $x_1$ and $x_2$ are the two real roots of the equation $x^2 + m^2x + n = 0$ (where $n < 0$), and $y_1$ and $y_2$ are the two real roots of the equation $y^2 + 5my + 7 = 0$. Also, it is known that $x_1 - y_1 = 2$ and $x_2 - y_2 = 2$. Find the value of $m$.

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