
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 $P$ be the parabola with equation $y = x^2$ and let $R = (10, -6)$. There are real numbers $a$ and $b$ such that the line through $R$ with slope $n$ does not intersect $P$ if and only if $a < n < b$. What is $a + b$?

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