
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
Is there a point \( P \) on the parabola given by the equation \( y = x^2 \) and a point \( Q \) on the parabola given by the equation \( y = 2x^2 - \frac{7}{2}x + \frac{57}{16} \) such that the segment \( PQ \) is perpendicular to the parabolas \( p \) and \( q \)? (By the angle at the intersection of a parabola and a line intersecting it, we mean the angle formed by the tangent to the parabola at the point of intersection and the intersecting line.)

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