
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
The numbers \( p \) and \( q \) are such that the parabolas \( y=-2x^{2} \) and \( y=x^{2}+px+q \) intersect at two points, enclosing a certain region.

Find the equation of the vertical line that divides the area of this region in half.

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