
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
A bead is placed on the curve $y = x^2 + 2x - 3$ at a point $P$ whose $y$-coordinate is $8$. It then slides along the curve to the nearest point $Q$ with a $y$-coordinate of $-1$. Determine the horizontal distance between $P$ and $Q$.
A) $3$
B) $3\sqrt{2}$
C) $3\sqrt{3}$
D) $6$
E) $2\sqrt{3}$

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