
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
Find two points \( P \) and \( Q \) on the curve \( y^2 = x \) such that the tangent line to the curve at point \( P \) is perpendicular to the line segment \( PQ \), and the angle between the tangent line to the curve at point \( Q \) and the line segment \( PQ \) is \( \frac{\pi}{4} \). (Draw a rough sketch).

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