
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
Given $19 P Q$ is any chord passing through the focus of a given parabola, $M$ and $N$ are the projections of $P$ and $Q$, respectively, on the directrix $l$, determine the relationship between the lateral surface area of the solid formed by rotating the broken line $M P Q N$ around $l$ and the surface area of the sphere with $P Q$ as its diameter.

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