
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 $L(m)$ be the x-coordinate of the left intersection point of the curves $y = x^2 - 6$ and $y = m$ (where $-6 < m < 6$), and $r = \frac{L(-m) - L(m)}{m}$, find the value of $r$ as $m$ approaches 0.

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