
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
Consider the parabola $y = x^2 - 4$ and a horizontal line $y = m$, where $-4 < m < 4$. Let $L(m)$ be the $x$-coordinate of the left endpoint of their intersection. Define \( r = \frac{L(-m) - L(m)}{m} \). Determine the value of $r$ as $m$ approaches zero.
A) $0$
B) $\frac{1}{4}$
C) $\frac{1}{2}$
D) $1$
E) $\frac{1}{\sqrt{4}}$

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