
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
Draw a perpendicular line to the tangent of a parabola at the point of tangency, and intersect this line with a line passing through the focus and parallel to the tangent.

What is the geometric locus of the points of intersection as the point of tangency moves along the parabola?

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