
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
In a parabola, draw a tangent at a variable point $M$ and then draw a perpendicular line $e$ through the vertex of the parabola. This line $e$ intersects the line $MF$ at point $P$, where $F$ is the focus of the parabola. What is the locus of point $P$?

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