
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 particle is placed on the parabola \( y = x^2 - x - 2 \) at a point \( P \) whose y-coordinate is \( 10 \). It is allowed to roll along the parabola until it reaches the nearest point \( Q \) whose y-coordinate is \( 0 \). The horizontal distance traveled by the particle (the numerical value of the difference in the x-coordinates of \( P \) and \( Q \)) is:
A) 1
B) 2
C) 3
D) 4 
E) 5

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