
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  $p$  be a real constant. The parabola  $y^2=-4px$  rolls without slipping around the parabola  $y^2=4px$ . Find the equation of the locus of the vertex of the rolling parabola.

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