
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
Let $L(m)$ be the $x$ coordinate of the left endpoint of the intersection of the graphs of $y = x^2 - 8$ and $y = m$, where $-8 < m < 8$. Determine the value of $r = [L(-m) - L(m)]/m$ as $m$ becomes arbitrarily close to zero.

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