
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
Let \( C \) be a parabola. Take points \( P \) and \( Q \) on \( C \) such that (1) \( PQ \) is perpendicular to the tangent at \( P \), (2) the area enclosed by the parabola and \( PQ \) is as small as possible. What is the position of the chord \( PQ \)?

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